Series Circuits Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

Three resistors with values of $10\ \Omega$ , $15\ \Omega$ , and $25\ \Omega$ are connected in series across a direct current (DC) voltage source. What is the total equivalent resistance of the circuit?

4.8\ \Omega

50\ \Omega

25\ \Omega

50\text{ k}\Omega

Show answer & explanation

Answer: $50\ \Omega$

Answer

The total equivalent resistance is

50\ \Omega

.

In a series circuit, electrical current flows through each component sequentially along a single path. Therefore, the total opposition to current flow is the sum of the individual resistor values:

R_T = 10\ \Omega + 15\ \Omega + 25\ \Omega = 50\ \Omega

.

Step-by-Step Solution

1

Identify the circuit configuration and the formula for total series resistance.

R_T = R_1 + R_2 + R_3

In a series circuit, there is only one continuous path for electric current, meaning the opposition to current flow is cumulative.

2

Substitute the given resistor values into the series formula.

R_T = 10\ \Omega + 15\ \Omega + 25\ \Omega

Each component contributes its full resistive value directly to the total opposition.

3

Calculate the arithmetic sum.

R_T = 50\ \Omega

Simple addition yields the equivalent circuit resistance.

Key Concept

In a series circuit, total equivalent resistance (

R_T

) equals the direct sum of all individual resistances (

R_T = R_1 + R_2 + \dots + R_n

).

Estimated Time:45s

Question 2Question →

Complete the statement regarding the fundamental electrical behavior of a series circuit.

Fill in the blanks below

In a series circuit, because all electrical components are connected end-to-end in a single continuous path, the electric is the same at every point throughout the circuit.

Show answer & explanation

Answer

current (or amperage)

In any series circuit, electrical components share a single continuous conductive loop. Under the principle of conservation of electric charge, the rate at which charge passes through any cross-section of the conductor (current) must be identical at all points (

I_{\text{total}} = I_1 = I_2

).

Step-by-Step Solution

1

Analyze the structural path of a series circuit.

A series circuit consists of a single closed loop with no branch points or alternate paths.

By definition, components in series are connected sequentially in one continuous line.

2

Apply the law of conservation of charge to determine which parameter remains constant across all components.

The rate of electron flow must be equal across all parts of the circuit (

I_{\text{total}} = I_1 = I_2 = \dots

).

Because charge cannot accumulate or disappear at any junction in a single loop, current is uniform everywhere.

Key Concept

Electric current is identical at all points in a series circuit because there is only one pathway for charge to flow.

Estimated Time:30s

Question 3Question →

A $24\text{ V}$ direct current (DC) power supply is connected to a circuit with two resistors in series: a $4\ \Omega$ resistor and an $8\ \Omega$ resistor. What is the current flowing through the $8\ \Omega$ resistor?

3\text{ A}

2\text{ A}

6\text{ A}

9\text{ A}

Show answer & explanation

Answer: $2\text{ A}$

Answer

2\text{ A}

The total resistance of the series circuit is the direct sum of the resistors (

4\ \Omega + 8\ \Omega = 12\ \Omega

). According to Ohm's Law (

I = V / R

), dividing the

24\text{ V}

source by

12\ \Omega

yields a total current of

2\text{ A}

. Because a series circuit provides only a single continuous path for electron flow, the current is identical through every component in the loop, meaning

2\text{ A}

flows through the

8\ \Omega

resistor.

Step-by-Step Solution

1

Calculate the total equivalent resistance of the series circuit.

R_{\text{total}} = R_1 + R_2 = 4\ \Omega + 8\ \Omega = 12\ \Omega

In any series circuit, individual resistances add directly together to form the total circuit resistance.

2

Apply Ohm's Law to determine the total circuit current.

I_{\text{total}} = \frac{V_{\text{total}}}{R_{\text{total}}} = \frac{24\text{ V}}{12\ \Omega} = 2\text{ A}

Current equals total voltage divided by total resistance.

3

Determine the current flowing specifically through the

8\ \Omega

resistor.

I_{R2} = I_{\text{total}} = 2\text{ A}

In a single-loop series circuit, current is uniform at all points and through all components.

Key Concept

Series Circuit Current and Total Resistance

Estimated Time:45s

Question 4Question →

Match each series circuit electrical property or condition on the left with its correct fundamental rule on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Circuit Current matches 'Remains identical and continuous through every connected component'; Total Resistance matches 'Equals the direct sum of all individual component resistances'; Source Voltage matches 'Divides across components such that individual drops sum to the source total'; Open Component Fault matches 'Completely interrupts electron flow throughout the entire single loop'.

Each relationship reflects the core principles of series circuit analysis: a single pathway guarantees uniform current throughout, sequential resistive elements add directly to total opposition, the sum of individual voltage drops balances the source voltage, and any break disrupts the entire closed conductive loop.

Step-by-Step Solution

1

Analyze current flow in a single-loop circuit

Identify that charge has only one path to follow, making current uniform throughout all series components.

Conservation of charge dictates current cannot accumulate or branch without alternative parallel paths.

2

Determine total resistance formula for series elements

Establish that each resistor adds directly to the total opposition (

R_T = R_1 + R_2 + \dots

).

Electrons must push through each resistive element sequentially.

3

Analyze voltage division across series loads

Confirm that source voltage is distributed proportionally across loads, summing to

V_T

.

Energy provided by the power supply equals total energy dropped across the circuit loads.

4

Evaluate the effect of a break or open circuit

Conclude that an open element halts all current in the entire circuit.

Breaking the single loop prevents complete continuity back to the power source.

Key Concept

Fundamental Series Circuit Laws (Current Uniformity, Resistance Additivity, Voltage Division, and Loop Continuity)

Estimated Time:45s

Question 5Question →

A direct current ( $12\text{ V}$ DC) circuit contains two indicator lamps connected in series. If a voltmeter measures a $7\text{ V}$ drop across the first lamp, what is the voltage drop across the second lamp?

12\text{ V}

5\text{ V}

7\text{ V}

19\text{ V}

Show answer & explanation

Answer: $5\text{ V}$

Answer

The voltage drop across the second lamp is

5\text{ V}

.

In a series circuit, total voltage supplied by the source is distributed across all series components such that the sum of the individual voltage drops equals the source voltage (

V_{\text{total}} = V_1 + V_2

). Subtracting the

7\text{ V}

drop across the first lamp from the

12\text{ V}

total supply gives

5\text{ V}

across the second lamp.

Step-by-Step Solution

1

Identify the fundamental rule for voltage distribution in a series circuit.

The total supply voltage equals the sum of the individual voltage drops across each series load:

V_{\text{total}} = V_1 + V_2

.

According to Kirchhoff's Voltage Law, the algebraic sum of all voltages around any closed loop in a circuit must equal zero.

2

Substitute the known values into the equation and solve for the unknown voltage drop (

V_2

).

V_2 = V_{\text{total}} - V_1 = 12\text{ V} - 7\text{ V} = 5\text{ V}

.

Subtracting the known component voltage drop from the source voltage yields the remaining voltage dropped across the second component.

Key Concept

Series Voltage Distribution (Kirchhoff's Voltage Law)

Estimated Time:45s

Question 6Question →

In a series-connected aircraft instrument lighting circuit, three resistive elements have values of $15\ \Omega$ , $35\ \Omega$ , and $50\ \Omega$ . What is the total equivalent resistance of the circuit in ohms ( $\Omega$ )?

Show answer & explanation

Answer: 100

Answer

100 ohms (

\Omega

)

In a series circuit, total resistance is calculated by adding the individual resistance values together (

R_T = R_1 + R_2 + R_3

). Summing

15\ \Omega

,

35\ \Omega

, and

50\ \Omega

gives exactly

100\ \Omega

.

Step-by-Step Solution

1

Identify the formula for total resistance in a series circuit

R_T = R_1 + R_2 + R_3

In a series circuit, there is only one continuous path for current flow, making total opposition to current equal to the sum of all individual resistances.

2

Substitute the individual component values and calculate the sum

R_T = 15\ \Omega + 35\ \Omega + 50\ \Omega = 100\ \Omega

Adding the three series resistances yields the overall equivalent resistance.

Key Concept

Total resistance in a series circuit is equal to the direct sum of all individual resistances.

Estimated Time:45s

Question 7Question →

An electrical technician is inspecting a circuit containing three resistive heating elements wired in series with a direct current power source. If one of the heating elements burns out and creates an open circuit, what happens to the current in the circuit?

Current continues to flow at the same level through the other two heating elements.

Current flow stops completely throughout the entire circuit.

Current increases through the remaining heating elements due to reduced total resistance.

Current bypasses the broken heating element and creates a short circuit back to the source.

Show answer & explanation

Answer: Current flow stops completely throughout the entire circuit.

Answer

Current flow stops completely throughout the entire circuit.

In a series circuit, there is only one continuous path for electrical current to travel from the power source through all connected loads and back. When one component burns out, it creates a physical break in that single conductive path (an open circuit). Because current requires an uninterrupted closed loop, an open circuit anywhere in the series loop causes total current to drop to zero across all components.

Step-by-Step Solution

1

Identify the circuit topology and the path rule for series circuits.

In a series circuit, all electrical components are connected end-to-end to form a single continuous loop.

Current must flow sequentially through every component in the loop because there are no alternative branches.

2

Determine the electrical impact of a burned-out component.

A burned-out element creates an open circuit, creating a physical break with infinite electrical resistance (

R = \infty

).

Electrons require an uninterrupted conductive path to travel from one terminal of the power source to the other.

3

Apply Ohm's Law to calculate the resulting loop current.

The total circuit current drops to zero (

I = 0\text{ A}

).

According to Ohm's Law (

I = \frac{V}{R}

), an infinite resistance in the loop causes the current throughout the entire series circuit to drop to zero.

Key Concept

Single continuous conductive path and open circuit fault behavior in series circuits

Estimated Time:45s

Question 8Question →

Complete the statement describing how adding components affects a series circuit connected to a constant voltage source.

Fill in the blanks below

When an additional resistor is added in series to a circuit connected to a constant voltage source, the total circuit resistance will and the total current in the circuit will .

Show answer & explanation

Answer

increase (for total resistance) and decrease (for total current)

In a series circuit, all components share a single continuous path. The total equivalent resistance is the arithmetic sum of each individual resistance (

R_T = R_1 + R_2 + R_3

). Inserting an additional resistor increases the total circuit resistance. By Ohm's Law (

I = \frac{V}{R_T}

), an increase in total resistance with an unchanging source voltage results in a decrease in total current.

Step-by-Step Solution

1

Determine the effect of adding a resistor on total series resistance.

Total resistance increases.

In a series circuit, total resistance is the sum of all individual resistances (

R_T = R_1 + R_2 + \dots + R_n

), so adding another resistor always increases the total resistance.

2

Apply Ohm's Law to find the effect on total loop current with a fixed voltage source.

Total circuit current decreases.

According to Ohm's Law (

I = \frac{V}{R_T}

), when source voltage

V

remains constant and total resistance

R_T

increases, the total current

I

must decrease.

Key Concept

Series Resistance and Current Relationship

Alternative Method

Consider a numerical example: a

12\text{ V}

source with a single

6\ \Omega

resistor yields

I = \frac{12\text{ V}}{6\ \Omega} = 2\text{ A}

. Adding another

6\ \Omega

resistor in series makes

R_T = 12\ \Omega

, which drops current to

I = \frac{12\text{ V}}{12\ \Omega} = 1\text{ A}

.

Estimated Time:45s

Question 9Question →

In a direct current (DC) electronic device, two resistors with values of $30\ \Omega$ and $60\ \Omega$ are connected in series. What is the total equivalent resistance of this circuit?

90\ \Omega

20\ \Omega

30\ \Omega

1800\ \Omega

Show answer & explanation

Answer: $90\ \Omega$

Answer

90\ \Omega

The total resistance of a series circuit is the sum of the individual component resistances (

R_T = R_1 + R_2

). Adding

30\ \Omega

and

60\ \Omega

gives

90\ \Omega

.

Step-by-Step Solution

1

Identify the formula for total resistance in a series circuit.

R_T = R_1 + R_2

In a series circuit, current flows through each resistor sequentially, meaning total opposition to current is the sum of all individual resistances.

2

Substitute the given resistor values into the series formula.

R_T = 30\ \Omega + 60\ \Omega = 90\ \Omega

Adding the individual resistor values produces the total equivalent resistance.

Key Concept

Total resistance in a series circuit equals the sum of all individual resistances (

R_T = R_1 + R_2 + \dots + R_n

).

Estimated Time:30s

Question 10Question →

Match each series circuit parameter or condition to its corresponding electrical rule.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Total Circuit Resistance pairs with 'Equal to the sum of the individual component resistances'; Circuit Current pairs with 'Remains constant and identical throughout all parts of the circuit'; Total Voltage pairs with 'Equal to the sum of all individual component voltage drops'; Open Circuit Condition pairs with 'Completely interrupts electron flow throughout the entire circuit loop'.

In a series circuit, electric charge has only one continuous loop to travel. Consequently, current is identical at every point, total resistance is the direct sum of all individual resistances, total voltage equals the sum of the individual component voltage drops, and an open circuit completely halts current flow.

Step-by-Step Solution

1

Identify the resistance relationship in a single-path series circuit.

Total resistance is additive (

R_T = R_1 + R_2 + \dots

).

Electrons must travel through each resistive element sequentially, adding together their opposition to current.

2

Identify the current behavior in a series circuit.

Current is uniform everywhere (

I_T = I_1 = I_2

).

There are no branch splits or junctions, so the rate of charge flow is constant throughout the single loop.

3

Identify how voltage is distributed across a series circuit.

Source voltage equals the sum of individual component voltage drops (

V_T = V_1 + V_2 + \dots

).

The total electrical potential provided by the power supply is completely dropped across the resistive elements.

4

Determine the effect of an open fault in a series circuit.

Current flow stops entirely throughout the circuit.

A break at any point opens the single continuous conductive pathway required for current to flow.

Key Concept

Series Circuit Fundamental Rules

Estimated Time:45s

Question 11Question →

An auxiliary automotive circuit connects a $12\ \text{V}$ direct current (DC) power source in series with two resistors valued at $2\ \Omega$ and $4\ \Omega$ . What is the total current flowing through the circuit?

2\ \text{A}

9\ \text{A}

0.5\ \text{A}

72\ \text{A}

Show answer & explanation

Answer: $2\ \text{A}$

Answer

The total current flowing through the circuit is

2\ \text{A}

.

In a series circuit, total resistance is the direct sum of the individual resistors:

R_T = 2\ \Omega + 4\ \Omega = 6\ \Omega

. Using Ohm's law (

I = V / R_T

), dividing the source voltage of

12\ \text{V}

by the total resistance of

6\ \Omega

yields a total current of

2\ \text{A}

.

Step-by-Step Solution

1

Calculate the total equivalent resistance (

R_T

) of the series circuit.

R_T = R_1 + R_2 = 2\ \Omega + 4\ \Omega = 6\ \Omega

In a series circuit, total resistance equals the sum of all individual resistances.

2

Calculate the total circuit current (

I

) using Ohm's law.

I = \frac{V_T}{R_T} = \frac{12\ \text{V}}{6\ \Omega} = 2\ \text{A}

Ohm's law states that current equals voltage divided by total resistance.

Key Concept

Series Circuit Resistance and Ohm's Law

Estimated Time:45s

Question 12Question →

A $36\text{ V}$ DC power supply is connected across a series circuit containing a fixed $16\ \Omega$ resistor and a variable rheostat. If an in-line ammeter measures a circuit current of $1.5\text{ A}$ , what is the resistance setting of the rheostat?

24\ \Omega

8\ \Omega

54\ \Omega

9.6\ \Omega

Show answer & explanation

Answer: $8\ \Omega$

Answer

8\ \Omega

In a series circuit, the current is identical at all points. Applying Ohm's Law gives the total resistance:

R_T = \frac{V_T}{I} = \frac{36\text{ V}}{1.5\text{ A}} = 24\ \Omega

. Since resistances in series add together linearly (

R_T = R_{\text{fixed}} + R_{\text{rheostat}}

), the rheostat resistance is

24\ \Omega - 16\ \Omega = 8\ \Omega

.

Step-by-Step Solution

1

Calculate the total circuit resistance (

R_T

) using Ohm's Law.

R_T = \frac{V_T}{I} = \frac{36\text{ V}}{1.5\text{ A}} = 24\ \Omega

The current in a series circuit is uniform throughout the entire loop, allowing Ohm's Law to determine total loop resistance from total voltage and current.

2

Subtract the fixed resistance from the total series resistance to solve for the unknown rheostat resistance (

R_{\text{rheostat}}

).

R_{\text{rheostat}} = R_T - R_{\text{fixed}} = 24\ \Omega - 16\ \Omega = 8\ \Omega

In a series circuit, total resistance equals the sum of all individual resistances (

R_T = R_1 + R_2

).

Key Concept

Series Total Resistance and Ohm's Law

Estimated Time:1m 0s

Question 13Question →

A marine navigation console contains three indicator loads connected in series across a $75\text{ V}$ direct current (DC) power supply. The individual resistances of the loads are $8\ \Omega$ , $12\ \Omega$ , and $5\ \Omega$ . What is the total equivalent resistance of the circuit, and what is the current flowing through each individual load? Complete the statements below.

Fill in the blanks below

The total equivalent resistance of the series circuit is

\Omega

, and the current flowing through each load is

\text{A}

.

Show answer & explanation

Answer

The total equivalent resistance is

25\ \Omega

and the current through each load is

3\ \text{A}

.

In a series circuit, the total resistance is found by directly summing all individual component resistances (

8\ \Omega + 12\ \Omega + 5\ \Omega = 25\ \Omega

). Using Ohm's Law (

I = V / R_T

), the total circuit current is

75\text{ V} / 25\ \Omega = 3\text{ A}

. In any series circuit, the current is constant throughout the entire loop, meaning every connected component experiences the exact same

3\text{ A}

of current.

Step-by-Step Solution

1

Calculate the total equivalent resistance of the series circuit by adding the individual resistance values.

R_T = R_1 + R_2 + R_3 = 8\ \Omega + 12\ \Omega + 5\ \Omega = 25\ \Omega

In a series circuit, total resistance equals the arithmetic sum of all individual resistances in the loop.

2

Calculate the total circuit current using Ohm's Law (

I = V_T / R_T

).

I = \frac{75\text{ V}}{25\ \Omega} = 3\text{ A}

Ohm's Law defines current as total applied electromotive force divided by total series resistance.

3

Determine the current flowing through each individual component.

I_1 = I_2 = I_3 = I_T = 3\text{ A}

Because there is only one continuous path for charge flow in a series circuit, current is identical at all points.

Key Concept

Series Circuit Resistance and Current Characteristics

Estimated Time:1m 0s

Question 14Question →

An industrial automation control loop is powered by a $48\text{ V}$ direct current (DC) source connected in series with three resistors: $R_1 = 20\ \Omega$ , $R_2 = 50\ \Omega$ , and $R_3 = 90\ \Omega$ . What is the voltage drop across resistor $R_2$ ?

48\text{ V}

15\text{ V}

0.3\text{ V}

16\text{ V}

Show answer & explanation

Answer: $15\text{ V}$

Answer

The voltage drop across the

50\ \Omega

resistor (

R_2

) is

15\text{ V}

.

The correct answer is

15\text{ V}

. In a series circuit, the total resistance is the sum of all individual resistors:

20\ \Omega + 50\ \Omega + 90\ \Omega = 160\ \Omega

. The circuit current is therefore

48\text{ V} / 160\ \Omega = 0.3\text{ A}

. Applying Ohm's Law across

R_2

gives a voltage drop of

0.3\text{ A} \times 50\ \Omega = 15\text{ V}

.

Step-by-Step Solution

1

Calculate the total circuit resistance (

R_T

) by summing the three series resistances.

R_T = R_1 + R_2 + R_3 = 20\ \Omega + 50\ \Omega + 90\ \Omega = 160\ \Omega

In a series circuit, total resistance is the algebraic sum of all individual load resistances.

2

Determine the total circuit current (

I_T

) using Ohm's Law.

I_T = \frac{V_S}{R_T} = \frac{48\text{ V}}{160\ \Omega} = 0.3\text{ A}

Current equals total voltage divided by total resistance, and current remains constant through every component in a single series loop.

3

Calculate the specific voltage drop (

V_2

) across resistor

R_2

.

V_2 = I_T \times R_2 = 0.3\text{ A} \times 50\ \Omega = 15\text{ V}

Applying Ohm's Law (

V = I \times R

) to an individual component determines the potential difference dropped across that load.

Key Concept

Series circuit total resistance, current constancy, and individual component voltage drop calculation using Ohm's Law.

Estimated Time:1m 0s

Question 15Question →

In direct current (DC) electronics, circuit modifications and faults alter overall circuit parameters. Match each series circuit condition on the left with its correct electrical effect on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Adding a series resistor increases total resistance and decreases loop current; an open circuit drops current to zero; shorting a resistor reduces total resistance and increases current and remaining voltage drops; doubling source voltage doubles both total current and individual voltage drops.

In a series circuit, current flows through a single continuous path. Total resistance is the sum of all individual resistances (

R_T = R_1 + R_2 + \dots

). Adding a resistor increases total resistance, reducing current. Shorting a resistor bypasses that element, lowering total resistance and increasing loop current, which increases the voltage drop across the remaining resistors (

V = I \times R

). An open circuit breaks the loop, reducing current to zero. Doubling the source voltage across a fixed total resistance doubles the current and doubles each individual voltage drop proportionally.

Step-by-Step Solution

1

Analyze the resistance relationship for series circuits.

Total resistance is the direct sum of all individual resistors:

R_T = R_1 + R_2 + \dots + R_n

.

Adding a resistor increases

R_T

, while shorting out a resistor removes its resistance from the sum, lowering

R_T

.

2

Apply Ohm's Law (

I = \frac{V_T}{R_T}

) to determine current behavior under each modification.

Higher resistance reduces current, lower resistance increases current, and doubled voltage with fixed resistance doubles current.

Current is directly proportional to voltage and inversely proportional to total circuit resistance.

3

Evaluate the single-path property of a series circuit under open fault conditions.

An open circuit provides infinite resistance (

R = \infty

), causing

I = 0\text{ A}

.

A continuous closed path is mandatory for current flow in any series circuit.

Key Concept

Series Circuit Governing Rules and Fault Characteristics

Estimated Time:1m 15s

Question 16Question →

An emergency communications console is powered by a $120\text{ V}$ DC source connected in series with three resistive elements: $R_1 = 15\ \Omega$ , $R_2 = 25\ \Omega$ , and an unknown load resistor $R_3$ . If a voltmeter placed across $R_1$ reads $18\text{ V}$ , what is the resistance value of $R_3$ ?

85\ \Omega

60\ \Omega

100\ \Omega

104\ \Omega

Show answer & explanation

Answer: $60\ \Omega$

Answer

The resistance value of

R_3

is

60\ \Omega

.

In a series circuit, the current is identical at all points. Using Ohm's Law on the first resistor gives a loop current of

I = \frac{18\text{ V}}{15\ \Omega} = 1.2\text{ A}

. The total circuit resistance is

R_T = \frac{V_T}{I} = \frac{120\text{ V}}{1.2\text{ A}} = 100\ \Omega

. Since series resistances are additive (

R_T = R_1 + R_2 + R_3

), the unknown resistance is

R_3 = 100\ \Omega - (15\ \Omega + 25\ \Omega) = 60\ \Omega

.

Step-by-Step Solution

1

Calculate the common series circuit current using the known voltage drop and resistance of the first resistor.

I = \frac{V_1}{R_1} = \frac{18\text{ V}}{15\ \Omega} = 1.2\text{ A}

In a series circuit, current remains constant through every component.

2

Calculate the total equivalent resistance of the entire circuit using Ohm's Law with the total source voltage.

R_T = \frac{V_T}{I} = \frac{120\text{ V}}{1.2\text{ A}} = 100\ \Omega

Total resistance equals total supply voltage divided by the total circuit current.

3

Determine the resistance of the unknown resistor by subtracting the known resistors from the total series resistance.

R_3 = R_T - R_1 - R_2 = 100\ \Omega - 15\ \Omega - 25\ \Omega = 60\ \Omega

The total resistance in a series circuit is the linear sum of all individual resistances:

R_T = R_1 + R_2 + R_3

.

Key Concept

Series Circuit Analysis and Ohm's Law Multi-Step Synthesis

Estimated Time:1m 30s

Question 17Question →

A surveillance camera heating assembly is powered by a $120\text{ V}$ DC power supply connected in series with three heating elements: $R_1 = 18\ \Omega$ , $R_2 = 22\ \Omega$ , and $R_3 = 40\ \Omega$ . What is the voltage drop across the $22\ \Omega$ element ( $R_2$ )?

120\text{ V}

33\text{ V}

40\text{ V}

1.5\text{ V}

Show answer & explanation

Answer: $33\text{ V}$

Answer

33\text{ V}

In a series circuit, total equivalent resistance is the sum of all individual resistances (

18\ \Omega + 22\ \Omega + 40\ \Omega = 80\ \Omega

). Applying Ohm's Law with a

120\text{ V}

supply gives a uniform loop current of

1.5\text{ A}

(

120\text{ V} / 80\ \Omega

). Multiplying this current by the resistance of the specified component yields

1.5\text{ A} \times 22\ \Omega = 33\text{ V}

.

Step-by-Step Solution

1

Calculate the total series resistance (

R_T

) by summing individual resistances.

R_T = R_1 + R_2 + R_3 = 18\ \Omega + 22\ \Omega + 40\ \Omega = 80\ \Omega

In a series circuit, total resistance equals the sum of all individual resistances in the loop.

2

Determine the total circuit current (

I_T

) using Ohm's Law (

I = V / R

).

I_T = \frac{V_T}{R_T} = \frac{120\text{ V}}{80\ \Omega} = 1.5\text{ A}

Current remains constant through every component in a single continuous series loop.

3

Calculate the voltage drop (

V_2

) across the target resistor (

R_2 = 22\ \Omega

) using

V = I \times R

.

V_2 = I_T \times R_2 = 1.5\text{ A} \times 22\ \Omega = 33\text{ V}

The voltage drop across any individual series resistor is proportional to its resistance and the loop current.

Key Concept

Series Circuit Resistance and Voltage Division

Estimated Time:1m 0s

Question 18Question →

An aircraft cockpit lighting circuit is connected to a $24\text{ V}$ direct current (DC) power source. The circuit consists of three loads connected in series: a $15\ \Omega$ panel lamp, a $25\ \Omega$ dimming rheostat, and a $20\ \Omega$ ballast resistor. What is the voltage drop across the $25\ \Omega$ dimming rheostat in volts?

Show answer & explanation

Answer: 10

Answer

The voltage drop across the

25\ \Omega

dimming rheostat is

10\text{ V}

.

In a series circuit, the total resistance is the sum of all individual resistances:

15\ \Omega + 25\ \Omega + 20\ \Omega = 60\ \Omega

. Applying Ohm's Law to the entire circuit gives a current of

24\text{ V} / 60\ \Omega = 0.4\text{ A}

. Because current is constant throughout a series circuit, the voltage drop across the

25\ \Omega

rheostat is

0.4\text{ A} \times 25\ \Omega = 10\text{ V}

.

Step-by-Step Solution

1

Calculate the total series resistance (

R_T

) of the circuit.

R_T = 15\ \Omega + 25\ \Omega + 20\ \Omega = 60\ \Omega

In a series circuit, total resistance equals the algebraic sum of all individual series resistances.

2

Calculate the common series current (

I

) flowing through the circuit.

I = \frac{V_T}{R_T} = \frac{24\text{ V}}{60\ \Omega} = 0.4\text{ A}

Ohm's Law (

I = \frac{V}{R}

) relates the total supply voltage to the total circuit resistance.

3

Calculate the voltage drop (

V_2

) across the

25\ \Omega

resistor.

V_2 = I \times R_2 = 0.4\text{ A} \times 25\ \Omega = 10\text{ V}

Current is constant throughout all components in a series circuit, so the individual voltage drop is the product of loop current and component resistance.

Key Concept

In a series circuit, total resistance is the sum of individual resistances (

R_T = R_1 + R_2 + \dots + R_n

), current is identical through all components (

I_T = I_1 = I_2 = \dots = I_n

), and individual voltage drops are directly proportional to component resistance (

V_n = I \times R_n

).

Estimated Time:1m 0s

Question 19Question →

An aircraft avionics sensor circuit is powered by a $28\text{ V}$ direct current (DC) power source connected in series with three resistors: $R_1 = 30\ \Omega$ , $R_2 = 45\ \Omega$ , and an unknown resistor $R_3$ . A technician measures the voltage drop across $R_2$ and finds it to be $9\text{ V}$ . Based on these circuit measurements, what are the total loop current and the resistance value of $R_3$ ?

Fill in the blanks below

The total current flowing through the circuit is A, and the resistance value of

R_3

is

\Omega

.

Show answer & explanation

Answer

The circuit current is 0.2 A and the resistance of resistor R3 is 65 ohms.

Because the circuit components are connected in series, the current flowing through

R_2

(

I = 9\text{ V} / 45\ \Omega = 0.2\text{ A}

) is the exact same current passing through the entire loop. Applying Ohm's Law to the full circuit gives a total resistance of

R_T = 28\text{ V} / 0.2\text{ A} = 140\ \Omega

. Subtracting the known resistances (

30\ \Omega + 45\ \Omega = 75\ \Omega

) leaves

65\ \Omega

for

R_3

.

Step-by-Step Solution

1

Calculate the constant loop current using the known values for resistor

R_2

I = \frac{V_2}{R_2} = \frac{9\text{ V}}{45\ \Omega} = 0.2\text{ A}

In a series circuit, current is identical through every component.

2

Calculate the total equivalent resistance of the entire series circuit using Ohm's Law and the source voltage

R_T = \frac{V_{\text{source}}}{I} = \frac{28\text{ V}}{0.2\text{ A}} = 140\ \Omega

Total circuit resistance equals the total applied voltage divided by the common series current.

3

Determine the resistance of

R_3

by subtracting known series resistances from total resistance

R_3 = R_T - (R_1 + R_2) = 140\ \Omega - (30\ \Omega + 45\ \Omega) = 140\ \Omega - 75\ \Omega = 65\ \Omega

Total series resistance is the direct algebraic sum of all individual resistances in the loop.

Key Concept

In a single-loop series circuit, current is constant at all points (

I_T = I_1 = I_2 = I_3

), and total circuit resistance is the sum of all individual resistances (

R_T = R_1 + R_2 + R_3

).

Estimated Time:1m 15s

Question 20Question →

A military vehicle communication module is powered by a $60\text{ V}$ DC supply connected in series with three resistive components: a fixed input resistor $R_1 = 40\ \Omega$ , an unknown matching resistor $R_2$ , and a load resistor $R_3 = 80\ \Omega$ . If a technician measures a voltage drop of $12\text{ V}$ across resistor $R_1$ , what is the resistance value of $R_2$ ?

40\ \Omega

160\ \Omega

80\ \Omega

200\ \Omega

Show answer & explanation

Answer: $80\ \Omega$

Answer

80\ \Omega

Because current is uniform throughout a single series path, the current through the entire circuit is determined by the known component

R_1

:

I = \frac{12\text{ V}}{40\ \Omega} = 0.3\text{ A}

. With a

60\text{ V}

supply, the total circuit resistance is

R_T = \frac{60\text{ V}}{0.3\text{ A}} = 200\ \Omega

. Since

R_T = R_1 + R_2 + R_3

, subtracting the known values gives

R_2 = 200\ \Omega - 40\ \Omega - 80\ \Omega = 80\ \Omega

.

Step-by-Step Solution

1

Calculate the common series loop current using Ohm's Law across the first known resistor.

I = \frac{V_1}{R_1} = \frac{12\text{ V}}{40\ \Omega} = 0.3\text{ A}

In a series circuit, the current is identical at all points along the loop.

2

Calculate the total equivalent resistance of the circuit using the total supply voltage and loop current.

R_T = \frac{V_{\text{total}}}{I} = \frac{60\text{ V}}{0.3\text{ A}} = 200\ \Omega

Ohm's Law relates the source voltage to the total circuit resistance and total current.

3

Subtract the known series resistances from the total circuit resistance to isolate the unknown resistor.

R_2 = R_T - R_1 - R_3 = 200\ \Omega - 40\ \Omega - 80\ \Omega = 80\ \Omega

Total resistance in a series circuit is the algebraic sum of all individual resistances (

R_T = R_1 + R_2 + R_3

).

Key Concept

In a series circuit, current remains constant through every component, and total circuit resistance is the sum of individual resistances (

R_T = R_1 + R_2 + R_3

).

Alternative Method

Find the loop current

I = \frac{12\text{ V}}{40\ \Omega} = 0.3\text{ A}

. Then find the voltage drop across

R_3

:

V_3 = 0.3\text{ A} \times 80\ \Omega = 24\text{ V}

. Using Kirchhoff's Voltage Law, find the voltage drop across

R_2

:

V_2 = 60\text{ V} - 12\text{ V} - 24\text{ V} = 24\text{ V}

. Finally, calculate

R_2 = \frac{V_2}{I} = \frac{24\text{ V}}{0.3\text{ A}} = 80\ \Omega

.

Estimated Time:1m 30s

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