Inductors and Transformers Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

A technician is assembling a low-pass filter circuit and connects two inductors in series with values of $45\text{ mH}$ and $80\text{ mH}$ . Assuming there is no mutual magnetic coupling between the coils, what is the total equivalent inductance of the circuit in millihenries ( $\text{mH}$ )?

Show answer & explanation

Answer: 125

Answer

125

When inductors are connected in series without mutual inductance, their magnetic opposition to current changes accumulates directly, meaning the total inductance is simply the sum of the individual inductances (

45\text{ mH} + 80\text{ mH} = 125\text{ mH}

).

Step-by-Step Solution

1

Recall the formula for combining series inductances without mutual magnetic coupling.

L_{\text{total}} = L_1 + L_2

Like series resistors, total series inductance is the direct sum of individual inductances when there is no magnetic interaction.

2

Add the two individual inductance values together.

45\text{ mH} + 80\text{ mH} = 125\text{ mH}

Direct addition provides the equivalent total inductance in millihenries.

Key Concept

Inductors in series combine by direct addition, identical to the rule for resistors in series.

Estimated Time:45s

Question 2Question →

An inductor with an inductance of $2\text{ H}$ is connected across an alternating current ( $\text{AC}$ ) signal generator. If the generator frequency is doubled while maintaining a constant output voltage, how will the inductive reactance of the coil and the circuit current change?

The inductive reactance is halved, and the circuit current doubles.

The inductive reactance doubles, and the circuit current is halved.

The inductive reactance doubles, and the circuit current doubles.

The inductive reactance remains constant, and the circuit current drops to zero.

Show answer & explanation

Answer: The inductive reactance doubles, and the circuit current is halved.

Answer

The inductive reactance doubles, and the circuit current is halved.

Inductive reactance is defined by the relationship

X_L = 2\pi f L

. When the AC frequency (

f

) is doubled, the inductive reactance doubles because of their direct linear relationship. According to Ohm's law for AC circuits (

I = \frac{V}{X_L}

), increasing the total opposition by a factor of

2

at a constant voltage reduces the alternating current to half its original value.

Step-by-Step Solution

1

Determine the effect of frequency on inductive reactance

The inductive reactance (

X_L

) doubles.

Inductive reactance is calculated using the formula

X_L = 2\pi f L

. Since

X_L

is directly proportional to frequency (

f

), multiplying the frequency by

2

doubles the inductive reactance.

2

Determine the effect of changed reactance on circuit current using Ohm's law for AC circuits

The current (

I

) is reduced to one-half of its initial value.

Current in an inductive AC circuit is governed by

I = \frac{V}{X_L}

. With voltage (

V

) held constant, current is inversely proportional to inductive reactance (

X_L

). Doubling the reactance cuts the current in half.

Key Concept

Inductive Reactance and Frequency Relationship in AC Circuits

Estimated Time:1m 0s

Question 3Question →

An iron-core step-down transformer connected to a $240\text{ V AC}$ power line has $1{}200\text{ turns}$ in its primary winding and $150\text{ turns}$ in its secondary winding. The secondary winding is connected across a $15\ \Omega$ resistive load. Assuming an ideal transformer with no power losses, what is the current drawn by the primary winding from the AC source?

16.0\text{ A}

0.25\text{ A}

2.00\text{ A}

0.025\text{ A}

Show answer & explanation

Answer: $0.25\text{ A}$

Answer

0.25\text{ A}

The transformer has an

8:1

step-down turns ratio (

1{}200 / 150 = 8

). The secondary voltage is

240\text{ V} / 8 = 30\text{ V}

. Connecting a

15\ \Omega

resistor across

30\text{ V}

produces a secondary current of

30\text{ V} / 15\ \Omega = 2.0\text{ A}

. Since power in an ideal transformer is conserved (

P_p = P_s

), the primary current is stepped down by the same ratio:

2.0\text{ A} / 8 = 0.25\text{ A}

.

Step-by-Step Solution

1

Calculate the turns ratio (

a

) of the transformer.

a = \frac{N_p}{N_s} = \frac{1{}200\text{ turns}}{150\text{ turns}} = 8

The ratio of primary to secondary turns governs the voltage step-down and current step-up proportions.

2

Calculate the secondary voltage (

V_s

) across the load.

V_s = \frac{V_p}{a} = \frac{240\text{ V}}{8} = 30\text{ V}

In a step-down transformer, secondary voltage equals primary voltage divided by the turns ratio.

3

Calculate the secondary current (

I_s

) through the load resistor using Ohm's Law.

I_s = \frac{V_s}{R_L} = \frac{30\text{ V}}{15\ \Omega} = 2.0\text{ A}

Current through a resistive load is directly proportional to voltage and inversely proportional to resistance.

4

Calculate the primary current (

I_p

) drawn from the AC source.

I_p = \frac{I_s}{a} = \frac{2.0\text{ A}}{8} = 0.25\text{ A}

Conservation of power in an ideal transformer requires that

V_p I_p = V_s I_s

, meaning primary current is the secondary current divided by the turns ratio.

Key Concept

Ideal transformer transformation ratios (

N_p / N_s = V_p / V_s = I_s / I_p

)

Alternative Method

Using reflected impedance: The load resistance reflected to the primary side is

R_p' = a^2 \times R_L = 8^2 \times 15\ \Omega = 64 \times 15\ \Omega = 960\ \Omega

. The primary current is then directly calculated using Ohm's Law:

I_p = \frac{V_p}{R_p'} = \frac{240\text{ V}}{960\ \Omega} = 0.25\text{ A}

.

Estimated Time:2m 0s

Question 4Question →

In an electronic filter circuit, two inductors with values $L_1 = 30\text{ mH}$ and $L_2 = 20\text{ mH}$ are connected in parallel. This parallel pair is connected in series with a third inductor $L_3 = 18\text{ mH}$ and a fourth inductor $L_4 = 10\text{ mH}$ . Assuming negligible mutual inductance between the coils, what is the total equivalent inductance of the circuit in millihenries ( $\text{mH}$ )?

Show answer & explanation

Answer: 40

Answer

40 mH

The total inductance is

40\text{ mH}

. Inductors follow the same combination rules as resistors: the parallel pair (

30\text{ mH}

and

20\text{ mH}

) yields an equivalent inductance of

12\text{ mH}

, which when added to the series inductors (

18\text{ mH}

and

10\text{ mH}

) gives

12 + 18 + 10 = 40\text{ mH}

.

Step-by-Step Solution

1

Calculate the equivalent inductance of the two parallel inductors

L_1

and

L_2

.

L_p = \frac{L_1 \times L_2}{L_1 + L_2} = \frac{30\text{ mH} \times 20\text{ mH}}{30\text{ mH} + 20\text{ mH}} = \frac{600}{50} = 12\text{ mH}

Inductors in parallel combine using reciprocal addition, identically to resistors in parallel.

2

Calculate the total circuit inductance by summing the parallel combination with the remaining series inductors

L_3

and

L_4

.

L_{total} = L_p + L_3 + L_4 = 12\text{ mH} + 18\text{ mH} + 10\text{ mH} = 40\text{ mH}

Inductors in series combine via direct addition because the magnetic fields and induced voltages add along the common current path.

Key Concept

Inductors combine like resistors: series inductances add directly, while parallel inductances combine using reciprocal addition.

Estimated Time:1m 30s

Question 5Question →

A power adapter uses a step-down transformer with $400\text{ turns}$ on the primary coil and $20\text{ turns}$ on the secondary coil. If an input voltage of $120\text{ V AC}$ is applied across the primary coil, what is the secondary output voltage in volts?

Show answer & explanation

Answer: 6

Answer

The secondary output voltage is

6\text{ V}

.

In a transformer, the ratio of secondary voltage to primary voltage equals the ratio of secondary turns to primary turns (

V_s / V_p = N_s / N_p

). With

400

primary turns and

20

secondary turns, the turns ratio is

20 / 400 = 1/20

. Multiplying the primary voltage (

120\text{ V}

) by

1/20

yields a secondary output voltage of

6\text{ V}

.

Step-by-Step Solution

1

Identify the given transformer parameters from the problem statement.

V_p = 120\text{ V}

,

N_p = 400\text{ turns}

, and

N_s = 20\text{ turns}

.

These parameters are required to determine the relationship between primary and secondary voltages.

2

Set up the transformer turns ratio equation relating primary and secondary voltages to coil turns.

\frac{V_s}{V_p} = \frac{N_s}{N_p}

The voltage induced across a transformer winding is directly proportional to the number of turns in that winding.

3

Substitute the known values into the equation and compute the secondary voltage

V_s

.

V_s = 120\text{ V} \times \left(\frac{20}{400}\right) = 120\text{ V} \times 0.05 = 6\text{ V}

Direct algebraic calculation yields the step-down output voltage.

Key Concept

Transformer Turns Ratio and Voltage Transformation

Estimated Time:45s

Question 6Question →

A step-up transformer in a specialized power supply is connected to a $120\text{ V AC}$ source on its primary side. The secondary circuit delivers a current of $24\text{ mA}$ across a $25\text{ k}\Omega$ resistive load. If the primary winding has $150\text{ turns}$ , what is the total number of turns on the secondary winding?

30\text{ turns}

75\text{ turns}

750\text{ turns}

18\text{ turns}

Show answer & explanation

Answer: $750\text{ turns}$

Answer

750\text{ turns}

The correct answer is

750\text{ turns}

. First, determine the secondary voltage using Ohm's Law:

V_s = I_s \times R_L = (0.024\text{ A}) \times (25{}000\,\Omega) = 600\text{ V}

. Then, apply the transformer ratio formula

\frac{N_s}{N_p} = \frac{V_s}{V_p}

, yielding

N_s = 150 \times \left(\frac{600}{120}\right) = 750\text{ turns}

.

Step-by-Step Solution

1

Calculate the secondary voltage (

V_s

) across the load resistor using Ohm's Law (

V = I \times R

).

V_s = (24\text{ mA}) \times (25\text{ k}\Omega) = (0.024\text{ A}) \times (25{}000\,\Omega) = 600\text{ V}

Determining the voltage across the secondary winding is necessary to establish the transformer's voltage transformation ratio.

2

Apply the transformer turns ratio equation that relates winding turns directly to voltage.

\frac{N_s}{N_p} = \frac{V_s}{V_p}

In an ideal transformer, the ratio of secondary-to-primary turns is directly proportional to the ratio of secondary-to-primary voltage.

3

Substitute the known values (

V_s = 600\text{ V}

,

V_p = 120\text{ V}

, and

N_p = 150\text{ turns}

) to solve for the secondary turns (

N_s

).

N_s = 150 \times \left(\frac{600\text{ V}}{120\text{ V}}\right) = 150 \times 5 = 750\text{ turns}

Multiplying the primary turns by the voltage scaling factor gives the required secondary turns.

Key Concept

Transformer turns ratio and multi-step AC secondary load calculations

Estimated Time:2m 0s

Question 7Question →

An ideal transformer has a primary coil with $600$ turns and a secondary coil with $150$ turns. The primary coil is connected to a $120\text{ V}$ AC source, and the secondary coil is connected to a load consisting of two $15\ \Omega$ resistors wired in parallel. What is the total current flowing through the primary coil?

1\text{ A}

16\text{ A}

4\text{ A}

0.25\text{ A}

Show answer & explanation

Answer: $1\text{ A}$

Answer

The total current flowing through the primary coil is

1\text{ A}

.

The correct answer synthesizes multiple principles. First, the transformer step-down ratio is

600:150

, or

4:1

. This drops the primary

120\text{ V}

to a secondary

30\text{ V}

. Next, the two

15\ \Omega

resistors in parallel create an equivalent resistance of

7.5\ \Omega

. Using Ohm's Law (

I = V/R

), the secondary current is

30\text{ V} / 7.5\ \Omega = 4\text{ A}

. Finally, because a transformer steps current inversely to voltage, a

4:1

voltage step-down means a

1:4

current step-up from primary to secondary. Therefore, the primary current is

4\text{ A} / 4 = 1\text{ A}

.

Step-by-Step Solution

1

Calculate the turns ratio to determine the secondary voltage.

N_p/N_s = 600/150 = 4

. Therefore,

V_s = 120\text{ V} / 4 = 30\text{ V}

.

In a transformer, the voltage ratio is directly proportional to the turns ratio.

2

Determine the equivalent resistance of the secondary load.

For two equal resistors in parallel,

R_{eq} = 15\ \Omega / 2 = 7.5\ \Omega

.

Parallel branches provide multiple paths for current, reducing the total resistance of the circuit.

3

Apply Ohm's law to find the total secondary current.

I_s = V_s / R_{eq} = 30\text{ V} / 7.5\ \Omega = 4\text{ A}

.

The total current drawn by the load depends on the secondary voltage and the equivalent resistance of the load.

4

Calculate the primary current using the inverse turns ratio.

I_p = I_s / (N_p / N_s) = 4\text{ A} / 4 = 1\text{ A}

.

In an ideal transformer, power is conserved (

P_p = P_s

). If voltage steps down by a factor of 4, the current must step up by a factor of 4 from primary to secondary, making the primary current 1/4 of the secondary current.

Key Concept

Transformer turns ratio scaling for voltage and current, combined with parallel circuit analysis.

Question 8Question →

Match each magnetic component type to its primary operational characteristic and circuit application.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Air-core inductor matches with eliminating core saturation and hysteresis losses; Ferrite-core toroidal inductor matches with confining magnetic flux within a closed circular path to minimize EMI; Center-tapped step-down transformer matches with supplying two equal-magnitude, out-of-phase AC voltages; Variable autotransformer matches with utilizing a single continuous tapped winding without galvanic isolation.

Each component is correctly matched according to its electromagnetic construction: air-core inductors avoid high-frequency magnetic core losses; toroidal ferrite inductors contain magnetic flux to limit EMI; center-tapped transformers yield balanced dual out-of-phase secondary voltages; and autotransformers perform voltage adjustments via a single shared winding without galvanic isolation.

Step-by-Step Solution

1

Analyze core material and geometry impacts on the inductor types.

Air lacks ferromagnetic material, meaning it cannot saturate or exhibit core losses at RF frequencies (identifying the air-core inductor). A toroid geometry forms a closed magnetic loop that keeps magnetic fields contained to prevent EMI (identifying the toroidal ferrite inductor).

Inductor core selection balances permeability, saturation limits, operating frequency, and stray field radiation.

2

Analyze winding arrangements and isolation properties for the transformer types.

A center-tapped secondary winding produces two equal-amplitude outputs that are

180^\\circ

out of phase relative to the center tap (identifying the center-tapped transformer). An autotransformer uses a single tapped winding shared between input and output, which eliminates electrical isolation (identifying the variable autotransformer).

Winding configuration determines output phase symmetry and whether galvanic isolation exists between input and output circuits.

Key Concept

Operational characteristics, core geometries, and winding configurations of inductors and transformers

Estimated Time:1m 30s

Question 9Question →

Which of the following best describes the primary function of an inductor in an electronic circuit?

Opposing changes in electric current by storing energy in a magnetic field

Opposing changes in voltage by storing energy in an electrostatic field

Converting alternating current (AC) directly into steady direct current (DC)

Stepping up direct current (DC) voltage without requiring a fluctuating magnetic flux

Show answer & explanation

Answer: Opposing changes in electric current by storing energy in a magnetic field

Answer

Opposing changes in electric current by storing energy in a magnetic field

An inductor is an electrical component designed to store energy within an electromagnetic field generated by current flowing through its coils. Due to self-inductance, it produces an opposing electromotive force whenever current changes, thereby resisting rapid current variations.

Step-by-Step Solution

1

Identify the fundamental physical construction and behavior of an inductor.

An inductor is made of wire coiled around a core (air, iron, or ferrite).

When electric current passes through the coil, Ampere's law dictates that a magnetic field develops around the conductor.

2

Determine how the component reacts to dynamic circuit conditions.

According to Lenz's Law and Faraday's Law of Induction, any change in current produces a counter-electromotive force (back EMF) that opposes that change.

This property gives inductors their key application as chokes and energy storage devices in magnetic fields.

Key Concept

Inductors store energy in a magnetic field and oppose changes in electric current.

Estimated Time:40s

Question 10Question →

In electronics, inductors and transformers rely on magnetic fields to store energy, filter signals, and modify alternating current voltages. Match each component term to its correct definition or operational characteristic.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Henry (H) matches the standard unit of electrical inductance in a coil; Ferrite Core matches a magnetic ceramic material used in high-frequency coils to minimize energy losses; Step-up Transformer matches a device with more secondary turns than primary turns that increases output AC voltage; Inductive Reactance matches the opposition an inductor offers to the flow of alternating current, measured in ohms.

Each concept accurately pairs with its standard electronic definition: Henry (H) is the unit of inductance; Ferrite Core is the high-frequency ceramic magnetic material; Step-up Transformer increases output AC voltage via greater secondary turns; and Inductive Reactance is the coil's opposition to AC current measured in ohms.

Step-by-Step Solution

1

Identify the standard unit of measurement for inductance

The Henry (H) is the standard unit of inductance.

Inductance measures a coil's ability to induce back-EMF opposing current changes, measured in henries.

2

Identify the specialized core material used for high frequencies

Ferrite core matches the ceramic magnetic material.

Ferrite reduces eddy current losses at radio and high frequencies due to its high electrical resistivity.

3

Identify the transformer type that raises alternating voltage

A step-up transformer increases output voltage.

By the turns ratio principle, having more secondary turns than primary turns increases secondary AC voltage.

4

Identify the property representing opposition to AC current in ohms

Inductive reactance represents AC opposition in ohms.

Inductive reactance (

X_L = 2\pi f L

) quantifies how much an inductor restricts alternating current at a given frequency.

Key Concept

Basic terminology, units, materials, and operating principles of inductors and transformers.

Alternative Method

Recall standard electronic abbreviations and formulas:

L

is measured in Henries (H),

X_L

is measured in Ohms (

\Omega

), and

N_s > N_p

signifies a step-up voltage transformer.

Estimated Time:45s

Question 11Question →

A technician installs an inductor (choke) in series with the output line of a direct current (DC) power supply to filter out residual alternating current (AC) ripple. What is the primary effect of the inductor on this electrical current?

It completely blocks steady direct current while allowing alternating current ripple to pass freely.

It steps up the fluctuating AC voltage into a higher voltage DC output through mutual induction.

It opposes rapid changes in current, resisting the AC ripple while allowing steady DC to pass with minimal resistance.

It dissipates both AC ripple and steady DC current equally as thermal heat by acting as a pure resistor.

Show answer & explanation

Answer: It opposes rapid changes in current, resisting the AC ripple while allowing steady DC to pass with minimal resistance.

Answer

The inductor opposes rapid current variations (the AC ripple) due to inductive reactance while allowing steady direct current (DC) to pass freely.

An inductor resists changes in current through self-induction. When placed in series with a DC power supply line, its inductive reactance (

X_L = 2\pi f L

) creates significant opposition to the fluctuating AC ripple component while providing near-zero opposition to the constant DC current.

Step-by-Step Solution

1

Identify the fundamental operating principle of an inductor.

Inductors store energy in a magnetic field and inherently oppose any change in electrical current (

V_L = L \frac{di}{dt}

).

According to Lenz's Law, when current changes through a coil, a self-induced counter-electromotive force (CEMF) is produced that resists that change.

2

Analyze the inductor's frequency-dependent opposition (inductive reactance,

X_L

).

For steady DC (

f = 0\text{ Hz}

),

X_L = 2\pi f L = 0\,\Omega

, so DC passes with negligible opposition. For AC ripple (

f > 0\text{ Hz}

),

X_L > 0\,\Omega

, which impedes the fluctuation.

Higher frequency signals encounter significant inductive reactance, attenuating the unwanted AC ripple while letting constant DC through to the load.

Key Concept

Inductors oppose changes in alternating current via inductive reactance while allowing steady direct current to flow with minimal opposition.

Estimated Time:45s

Question 12Question →

A control transformer in an HVAC system steps down an input line voltage of $240\text{ V}$ AC to an output voltage of $24\text{ V}$ AC to safely power a thermostat circuit. If the primary winding consists of $800$ turns of wire, what is the number of turns on the secondary winding?

Show answer & explanation

Answer: 80

Answer

80 turns

The secondary winding requires 80 turns. According to the transformer turns ratio relationship,

\frac{V_p}{V_s} = \frac{N_p}{N_s}

. Since the secondary voltage (

24\text{ V}

) is one-tenth of the primary input voltage (

240\text{ V}

), the secondary coil must have one-tenth the number of turns of the primary coil:

800 \times 0.10 = 80

turns.

Step-by-Step Solution

1

Identify known electrical parameters from the problem statement.

V_p = 240\text{ V}

,

V_s = 24\text{ V}

, and

N_p = 800\text{ turns}

.

Establishing the input and output parameters is necessary to set up the transformer relationship.

2

Set up the ideal transformer turns ratio equation relating voltage and turns.

\frac{V_p}{V_s} = \frac{N_p}{N_s}

The voltage induced across transformer windings is directly proportional to the number of turns in each coil.

3

Rearrange the equation to isolate the unknown secondary winding turns (

N_s

).

N_s = N_p \times \left(\frac{V_s}{V_p}\right)

Algebraic isolation allows direct computation of secondary turns.

4

Substitute the known numerical values into the formula and calculate the result.

N_s = 800 \times \left(\frac{24\text{ V}}{240\text{ V}}\right) = 800 \times 0.10 = 80\text{ turns}

Carrying out the arithmetic yields the exact number of secondary turns required.

Key Concept

Transformer Turns Ratio and Voltage Transformation

Alternative Method

Calculate the turns-per-volt ratio of the primary coil:

\frac{800\text{ turns}}{240\text{ V}} = \frac{10}{3}\text{ turns/V}

. Then multiply by the desired secondary voltage:

24\text{ V} \times \frac{10}{3}\text{ turns/V} = 80\text{ turns}

.

Estimated Time:45s

Question 13Question →

In an electronic power system, two ideal transformers are cascaded (connected in sequence).

Transformer 1 receives an input voltage of $1{}200\text{ V AC}$ on its primary coil, which has $3{}000\text{ turns}$ . The secondary coil of Transformer 1 has $600\text{ turns}$ , and its output voltage is fed directly into the primary coil of Transformer 2.

Transformer 2 further steps down this voltage to supply exactly $48\text{ V AC}$ to an electronic load.

If the secondary coil of Transformer 2 contains $50\text{ turns}$ , how many turns must the primary coil of Transformer 2 have?

Show answer & explanation

Answer: 250

Answer

250 turns

The correct answer is derived by sequentially applying the transformer turns ratio formula (

V_p/V_s = N_p/N_s

) across the cascaded system. Transformer 1 operates with a 5:1 step-down ratio, reducing the

1{}200\text{ V}

input to

240\text{ V}

. Transformer 2 receives this

240\text{ V}

and must further step it down to

48\text{ V}

, which also requires a 5:1 ratio. Multiplying the

50

secondary turns by this ratio yields

250

primary turns.

Step-by-Step Solution

1

Calculate the secondary voltage of Transformer 1.

V_{s1} = 240\text{ V AC}

Using the turns ratio formula

V_{s1} / V_{p1} = N_{s1} / N_{p1}

, we find

V_{s1} = 1{}200 \times (600 / 3{}000) = 1{}200 \times 0.2 = 240\text{ V AC}

.

2

Identify the primary voltage of Transformer 2.

V_{p2} = 240\text{ V AC}

Because the transformers are cascaded in series, the output voltage of Transformer 1 serves directly as the input voltage for Transformer 2.

3

Set up the turns ratio equation for Transformer 2.

N_{p2} / 50 = 240 / 48

Applying the turns ratio formula

N_{p2} / N_{s2} = V_{p2} / V_{s2}

to the second transformer using its specific input and output voltages.

4

Solve for the primary turns of Transformer 2.

N_{p2} = 250\text{ turns}

N_{p2} = 50 \times (240 / 48) = 50 \times 5 = 250\text{ turns}

.

Key Concept

Cascaded Transformer Turns Ratios

Question 14Question →

A technician connects a step-up transformer to a $30\text{ V}$ AC power supply. The transformer has $200\text{ turns}$ on its primary winding and $800\text{ turns}$ on its secondary winding. Assuming ideal operating conditions with no energy losses, what is the output voltage at the secondary winding?

7.5\text{ V}

12\text{ V}

120\text{ V}

0\text{ V}

Show answer & explanation

Answer: $120\text{ V}$

Answer

The secondary output voltage is

120\text{ V}

.

For an ideal transformer, secondary voltage is calculated using the formula

V_s = V_p \times \left(\frac{N_s}{N_p}\right)

. Given a primary voltage of

30\text{ V}

and a turns ratio of

\frac{800}{200} = 4

, the secondary voltage is

30\text{ V} \times 4 = 120\text{ V}

.

Step-by-Step Solution

1

Identify the known values and the transformer voltage-turns relationship formula.

V_p = 30\text{ V}

,

N_p = 200\text{ turns}

,

N_s = 800\text{ turns}

, using

\frac{V_s}{V_p} = \frac{N_s}{N_p}

.

In an ideal transformer, the ratio of the secondary voltage to the primary voltage equals the ratio of secondary turns to primary turns.

2

Calculate the turns ratio (

N_s / N_p

).

\frac{800}{200} = 4

.

Finding the ratio simplifies multiplying the primary voltage to determine secondary voltage.

3

Multiply the primary input voltage by the turns ratio to find the secondary voltage (

V_s

).

V_s = 30\text{ V} \times 4 = 120\text{ V}

.

Since the secondary winding has four times as many turns as the primary, the secondary voltage must be four times greater than the primary voltage.

Key Concept

Transformer Turns and Voltage Ratio

Estimated Time:45s

Question 15Question →

Electromagnetic components are essential for controlling current and voltage levels in alternating current circuits. Which characteristic or operational principle correctly corresponds to each listed component or term?

Click a left item, then click its matching right item

Show answer & explanation

Answer

Step-up transformer matches a device with more secondary turns than primary turns that increases alternating voltage; Inductor matches a device that opposes rapid changes in electric current by storing energy in a magnetic field; Henry matches the standard unit of measurement for electrical inductance; Mutual induction matches the process by which a changing current in one coil induces an electromotive force in an adjacent coil.

Each item is matched to its exact operational role and definition: the step-up transformer increases AC voltage via a greater secondary turn count; the inductor resists current changes through magnetic storage; the henry serves as the unit of inductance; and mutual induction represents the principle of transferring energy across coupled coils.

Step-by-Step Solution

1

Identify the function of a step-up transformer.

A step-up transformer increases alternating voltage because its secondary winding has more turns than its primary winding (

N_s > N_p

).

According to the transformer turns ratio formula,

\frac{V_s}{V_p} = \frac{N_s}{N_p}

, higher secondary turns produce higher secondary voltage.

2

Identify the operating behavior of an inductor.

An inductor resists sudden current fluctuations by temporarily storing electrical energy in a concentrated magnetic field.

Lenz's law states that the induced back-EMF always acts to oppose the original change in current.

3

Identify the standard unit for inductance.

The henry (

\text{H}

) is the recognized unit of electrical inductance.

One henry of inductance induces an electromotive force of one volt when the current changes at a rate of one ampere per second.

4

Identify the definition of mutual induction.

Mutual induction is the magnetic coupling effect where current variations in a primary winding induce a voltage across a separate secondary winding.

This electromagnetic linkage allows electrical energy to transfer between isolated circuits without direct conductive contact.

Key Concept

Core definitions, units, and operational characteristics of inductors and transformers

Estimated Time:45s

Question 16Question →

A power supply circuit utilizes a step-down transformer to convert an alternating current (AC) input of $100\text{ V}$ to an output of $25\text{ V}$ . If the primary winding contains $400\text{ turns}$ , how many turns are on the secondary winding?

1{}600\text{ turns}

100\text{ turns}

25\text{ turns}

10\text{ turns}

Show answer & explanation

Answer: $100\text{ turns}$

Answer

100\text{ turns}

The correct answer is

100\text{ turns}

. According to the transformer turns ratio law, the ratio of secondary voltage to primary voltage equals the ratio of secondary turns to primary turns:

\frac{V_s}{V_p} = \frac{N_s}{N_p}

. Rearranging to solve for the secondary turns yields

N_s = N_p \times \left(\frac{V_s}{V_p}\right) = 400 \times \left(\frac{25}{100}\right) = 100\text{ turns}

. Since this is a step-down transformer (

100\text{ V}

down to

25\text{ V}

, a

4:1

step-down ratio), the secondary coil must have one-fourth the number of turns of the primary coil.

Step-by-Step Solution

1

Identify the given transformer parameters

Primary voltage

V_p = 100\text{ V}

, secondary voltage

V_s = 25\text{ V}

, primary turns

N_p = 400\text{ turns}

Extracting the known values is necessary to set up the turns ratio equation.

2

State the transformer voltage and turns ratio formula

\frac{V_p}{V_s} = \frac{N_p}{N_s} \implies N_s = N_p \times \left(\frac{V_s}{V_p}\right)

In an ideal transformer, the voltage across each winding is directly proportional to the number of turns.

3

Substitute the values and calculate the secondary winding turns

N_s = 400 \times \left(\frac{25\text{ V}}{100\text{ V}}\right) = 400 \times 0.25 = 100\text{ turns}

Performing the proportional calculation gives the exact number of secondary turns required.

Key Concept

Transformer Turns Ratio and Voltage Transformation

Estimated Time:45s

Question 17Question →

An AC step-down transformer has $600\text{ turns}$ on its primary winding and $50\text{ turns}$ on its secondary winding. The primary winding is connected to a $120\text{ V}$ AC source, and the secondary circuit delivers current to a load drawing $2.4\text{ A}$ . What is the current flowing in the primary winding?

28.8\text{ A}

20\text{ mA}

0.2\text{ A}

0\text{ A}

Show answer & explanation

Answer: $0.2\text{ A}$

Answer

0.2\text{ A}

In an ideal transformer, the ratio of primary current to secondary current is inversely proportional to the ratio of primary turns to secondary turns (

I_p / I_s = N_s / N_p

). Since the transformer has a

12:1

step-down turns ratio (

600/50 = 12

), the secondary voltage decreases by a factor of 12 while the primary current must be 12 times smaller than the secondary current:

I_p = 2.4\text{ A} / 12 = 0.2\text{ A}

.

Step-by-Step Solution

1

Determine the turns ratio between the primary and secondary windings

\frac{N_p}{N_s} = \frac{600}{50} = 12

The turns ratio determines both the voltage transformation ratio and the inverse current transformation ratio.

2

Apply the transformer current relationship to solve for primary current (

I_p

)

\frac{I_p}{I_s} = \frac{N_s}{N_p} \implies I_p = 2.4\text{ A} \times \frac{50}{600} = \frac{2.4\text{ A}}{12} = 0.2\text{ A}

In an ideal transformer, power in equals power out (

V_p I_p = V_s I_s

), which means current is inversely proportional to the number of turns.

Key Concept

Transformer Current and Turns Ratio Relationship

Estimated Time:1m 0s

Question 18Question →

An electronics technician connects three inductors in parallel across an AC filter circuit. The inductors have inductance values of $60\text{ mH}$ , $30\text{ mH}$ , and $20\text{ mH}$ , with negligible mutual inductance between them. What is the total equivalent inductance of the circuit in millihenries (mH)?

Show answer & explanation

Answer: 10

Answer

The total equivalent inductance of the parallel circuit is

10\text{ mH}

.

Inductors in parallel without mutual coupling combine according to the reciprocal formula

\frac{1}{L_{\text{total}}} = \frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{L_3}

. Computing

\frac{1}{60} + \frac{1}{30} + \frac{1}{20} = \frac{6}{60} = \frac{1}{10}

, and inverting yields

10\text{ mH}

.

Step-by-Step Solution

1

State the reciprocal formula for inductors connected in parallel

\frac{1}{L_{\text{total}}} = \frac{1}{L_1} + \frac{1}{L_2} + \frac{1}{L_3}

When inductors are in parallel and uncoupled, the total rate of current change is the sum of the individual branch rates, resulting in a reciprocal combination rule identical to parallel resistors.

2

Substitute the individual inductance values

\frac{1}{L_{\text{total}}} = \frac{1}{60} + \frac{1}{30} + \frac{1}{20}

Direct substitution of the known branch values:

L_1 = 60\text{ mH}

,

L_2 = 30\text{ mH}

, and

L_3 = 20\text{ mH}

.

3

Find the common denominator and sum the terms

\frac{1}{L_{\text{total}}} = \frac{1 + 2 + 3}{60} = \frac{6}{60} = \frac{1}{10}\text{ mH}^{-1}

Using the lowest common denominator (

60

) to perform fractional addition.

4

Invert the reciprocal to obtain equivalent inductance

L_{\text{total}} = 10\text{ mH}

Taking the reciprocal of

\frac{1}{10}\text{ mH}^{-1}

gives

10\text{ mH}

.

Key Concept

Parallel Inductance Calculation

Estimated Time:1m 0s

Question 19Question →

A step-down transformer has a $10:1$ turns ratio between its primary and secondary windings. If the primary winding is connected across a steady $12\text{ V}$ direct current (DC) power supply, what voltage is measured across the secondary winding under steady-state conditions?

1.2\text{ V}

12\text{ V}

0\text{ V}

120\text{ V}

Show answer & explanation

Answer: $0\text{ V}$

Answer

0\text{ V}

Transformers operate through mutual electromagnetic induction, requiring an alternating current (AC) to generate an expanding and collapsing magnetic field. A steady direct current (DC) produces a static, unvarying magnetic field once the circuit reaches steady state. Because Faraday's Law requires a changing magnetic field (

\frac{\Delta\Phi}{\Delta t} \neq 0

) to induce an electromotive force, the secondary winding produces exactly

0\text{ V}

.

Step-by-Step Solution

1

Identify the type of input voltage applied to the transformer primary winding.

The input source is a steady

12\text{ V}

direct current (DC) supply.

Transformers rely on mutual electromagnetic induction, which fundamentally requires a time-varying magnetic field.

2

Analyze the magnetic flux created in the core during steady-state DC operation.

A steady DC current produces a stationary, unchanging magnetic flux (

\frac{\Delta\Phi}{\Delta t} = 0

).

According to Faraday's Law of Induction, voltage is only induced in a conductor when magnetic flux lines expand or collapse across the winding turns.

3

Determine the resulting secondary output voltage.

The induced secondary voltage is

0\text{ V}

.

With zero rate of change of magnetic flux in steady state, no electromotive force (EMF) is induced in the secondary winding.

Key Concept

Transformers require alternating current (AC) to induce a secondary voltage via changing magnetic flux; steady direct current (DC) produces no secondary voltage.

Estimated Time:1m 0s

Question 20Question →

In electronic power and communication systems, various inductor and transformer configurations serve specialized functions. Match each inductive component on the left with its primary operational characteristic on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

RF Choke matches with presenting high opposition to high-frequency AC signals while allowing DC to pass; Isolation Transformer matches with providing a 1:1 turns ratio to electrically decouple circuits for safety; Air-Core Inductor matches with eliminating magnetic core losses at ultra-high frequencies; Step-Up Transformer matches with increasing alternating voltage while decreasing output current proportionally.

Each inductive device is matched according to its fundamental electromagnetic function: an RF choke blocks AC via inductive reactance while passing DC; an isolation transformer provides 1:1 galvanic isolation; an air-core inductor eliminates ferromagnetic core losses at high frequencies; and a step-up transformer increases voltage while proportionally reducing current.

Step-by-Step Solution

1

Identify the primary behavior of an RF choke

Recognized as a high-frequency AC blocking inductor that freely passes DC.

Inductive reactance (

X_L = 2\pi f L

) increases directly with frequency, creating significant impedance at radio frequencies.

2

Identify the function of an isolation transformer

Recognized as a 1:1 turns ratio transformer used for safety and ground-loop isolation.

Equal winding counts maintain input voltage on the secondary side while eliminating direct conductive connections.

3

Determine the main design advantage of an air-core inductor

Recognized as eliminating ferromagnetic core losses.

Without a solid iron or magnetic core, there are zero eddy currents or magnetic hysteresis losses at high frequencies.

4

Evaluate the voltage and current relationship of a step-up transformer

Recognized as increasing voltage while decreasing current proportionally.

Due to the principle of power conservation (

V_p I_p \approx V_s I_s

), increasing secondary voltage requires a corresponding drop in secondary current.

Key Concept

Operational characteristics and applications of inductors and transformers, including frequency-dependent choke behavior, core losses, galvanic isolation, and turns ratio power relationships.

Estimated Time:1m 0s

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