Ohm's Law Calculations and Concepts Practice Questions — Armed Services Vocational Aptitude Battery (ASVAB)

Question 1Question →

An electronics technician evaluates four separate direct current (DC) test circuits on a workbench. Match each circuit description on the left with its corresponding calculated electrical quantity on the right using Ohm's law ( $V = I \times R$ ).

Click a left item, then click its matching right item

Show answer & explanation

Answer

The circuit drawing

12\text{ mA}

at

48\text{ V}

matches a total resistance of

4\text{ k}\Omega

; the lamp with

250\text{ }\Omega

at

40\text{ mA}

matches a voltage drop of

10\text{ V}

; the

1.5\text{ k}\Omega

resistor at

30\text{ V}

matches a current of

20\text{ mA}

; and the

80\text{ }\Omega

relay coil at

24\text{ V}

matches a current of

300\text{ mA}

.

Each circuit scenario directly applies one variation of Ohm's law after properly adjusting metric units:

R = \frac{V}{I}

gives

4\text{ k}\Omega

,

V = I \times R

gives

10\text{ V}

, and

I = \frac{V}{R}

gives

20\text{ mA}

and

300\text{ mA}

respectively.

Step-by-Step Solution

1

Calculate resistance for the first circuit (

V = 48\text{ V}

,

I = 12\text{ mA}

)

R = \frac{48\text{ V}}{0.012\text{ A}} = 4{}000\text{ }\Omega = 4\text{ k}\Omega

Convert milliamperes to amperes (

12\text{ mA} = 0.012\text{ A}

) and apply Ohm's law formula

R = \frac{V}{I}

.

2

Calculate voltage across the lamp (

R = 250\text{ }\Omega

,

I = 40\text{ mA}

)

V = 0.040\text{ A} \times 250\text{ }\Omega = 10\text{ V}

Convert milliamperes to amperes (

40\text{ mA} = 0.040\text{ A}

) and apply

V = I \times R

.

3

Calculate current through the resistor (

V = 30\text{ V}

,

R = 1.5\text{ k}\Omega

)

I = \frac{30\text{ V}}{1{}500\text{ }\Omega} = 0.020\text{ A} = 20\text{ mA}

Convert kilohms to ohms (

1.5\text{ k}\Omega = 1{}500\text{ }\Omega

) and apply

I = \frac{V}{R}

, expressing the answer in milliamperes.

4

Calculate current through the relay coil (

V = 24\text{ V}

,

R = 80\text{ }\Omega

)

I = \frac{24\text{ V}}{80\text{ }\Omega} = 0.30\text{ A} = 300\text{ mA}

Apply

I = \frac{V}{R}

and convert amperes to milliamperes (

0.30\text{ A} = 300\text{ mA}

).

Key Concept

Ohm's law governs the fundamental mathematical relationship between electromotive force (voltage in volts), current (amperes), and opposition to current (resistance in ohms):

V = I \times R

,

I = \frac{V}{R}

, and

R = \frac{V}{I}

, with standard metric prefix conversions (

1\text{ k}\Omega = 1{}000\text{ }\Omega

,

1\text{ A} = 1{}000\text{ mA}

).

Estimated Time:1m 30s

Question 2Question →

A DC workbench circuit connected to a fixed-voltage power supply draws a current of $8\text{ mA}$ through a $1.5\text{ k}\Omega$ resistor. If the resistor is replaced with a $6.0\text{ k}\Omega$ resistor while the supply voltage remains unchanged, what is the new current flowing through the circuit?

32\text{ mA}

2\text{ mA}

12\text{ mA}

2\text{ A}

Show answer & explanation

Answer: $2\text{ mA}$

Answer

2\text{ mA}

The correct current is

2\text{ mA}

. First, applying Ohm's Law to the initial state yields a constant supply voltage of

V = I \times R = (8\text{ mA}) \times (1.5\text{ k}\Omega) = 12\text{ V}

. When the resistance increases to

6.0\text{ k}\Omega

, the new current is calculated as

I = \frac{V}{R} = \frac{12\text{ V}}{6.0\text{ k}\Omega} = 2\text{ mA}

. Proportional reasoning confirms this: quadrupling resistance at constant voltage reduces current to one-fourth of its initial value (

8\text{ mA} \div 4 = 2\text{ mA}

).

Step-by-Step Solution

1

Calculate the fixed supply voltage (

V

) using the initial current and resistance values.

V = I_1 \times R_1 = (8\text{ mA}) \times (1.5\text{ k}\Omega) = (0.008\text{ A}) \times (1500\ \Omega) = 12\text{ V}

Ohm's Law states that voltage is the product of current and resistance.

2

Calculate the new current (

I_2

) using the constant supply voltage and the new resistance value.

I_2 = \frac{V}{R_2} = \frac{12\text{ V}}{6.0\text{ k}\Omega} = \frac{12\text{ V}}{6000\ \Omega} = 0.002\text{ A} = 2\text{ mA}

Current equals voltage divided by resistance. Alternatively, since resistance increased by a factor of 4 (

1.5\text{ k}\Omega

to

6.0\text{ k}\Omega

) at constant voltage, current must decrease by a factor of 4 (

8\text{ mA} / 4 = 2\text{ mA}

).

Key Concept

Ohm's Law and inverse proportionality between current and resistance at constant voltage

Estimated Time:1m 0s

Question 3Question →

Match each circuit operating scenario on the left with its corresponding calculated electrical quantity on the right by applying Ohm's law and metric unit conversions.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The relay coil matches

50\text{ mA}

, the cockpit indicator matches

80\ \Omega

, the diagnostic probe matches

100\text{ V}

, and the automotive control module matches

5\text{ mA}

.

Each scenario correctly applies the relevant permutation of Ohm's law (

V=IR

,

I=V/R

, or

R=V/I

) following proper metric prefix conversion to base electrical units.

Step-by-Step Solution

1

Calculate the current for the relay coil

I = \frac{24\text{ V}}{480\ \Omega} = 0.05\text{ A} = 50\text{ mA}

Apply

I = \frac{V}{R}

directly and convert amperes to milliamperes by multiplying by

1000

.

2

Calculate the resistance for the aircraft indicator

R = \frac{28\text{ V}}{0.35\text{ A}} = 80\ \Omega

Convert

350\text{ mA}

to base units (

0.35\text{ A}

) and rearrange Ohm's law to

R = \frac{V}{I}

.

3

Calculate the voltage drop across the diagnostic probe

V = (40 \times 10^{-6}\text{ A}) \times (2.5 \times 10^{6}\ \Omega) = 100\text{ V}

Convert microamperes (

10^{-6}

) and megaohms (

10^{6}

) to standard base units and compute

V = I \times R

.

4

Calculate the current for the automotive control module

I = \frac{12\text{ V}}{2400\ \Omega} = 0.005\text{ A} = 5\text{ mA}

Convert

2.4\text{ k}\Omega

to

2400\ \Omega

, compute

I = \frac{V}{R}

, and express the result in milliamperes.

Key Concept

Ohm's Law calculations relating voltage (

V

), current (

I

), and resistance (

R

), integrated with metric prefix conversions.

Estimated Time:2m 0s

Question 4Question →

A marine communication device is connected to a $12\text{ V}$ direct current (DC) power source. If the circuit has a total resistance of $4\text{ }\Omega$ , what is the current flowing through the circuit in amperes ( $\text{A}$ )?

Show answer & explanation

Answer: 3

Answer

The current flowing through the circuit is

3\text{ A}

.

According to Ohm's law (

I = \frac{V}{R}

), the current in a direct current circuit is calculated by dividing the total voltage by the total circuit resistance. With a voltage of

12\text{ V}

across a resistance of

4\text{ }\Omega

, the current is

\frac{12\text{ V}}{4\text{ }\Omega} = 3\text{ A}

.

Step-by-Step Solution

1

Identify the given circuit parameters.

Voltage

V = 12\text{ V}

and resistance

R = 4\text{ }\Omega

.

Extracting the known quantities is necessary before applying the formula.

2

Select the appropriate form of Ohm's law to solve for current.

I = \frac{V}{R}

Ohm's law defines current as the ratio of electromotive force (voltage) to resistance.

3

Perform the division.

I = \frac{12}{4} = 3\text{ A}

Dividing

12\text{ V}

by

4\text{ }\Omega

computes the total current.

Key Concept

Ohm's law mathematical relationship where current is directly proportional to voltage and inversely proportional to resistance (

I = V / R

).

Estimated Time:45s

Question 5Question →

An avionics technician tests a DC monitoring circuit connected to a constant $450\text{ V}$ power supply. The circuit currently draws $25\text{ mA}$ of current. To meet new operating specifications, the current must be reduced to $9\text{ mA}$ . What is the required new resistance of the circuit?

50\,\Omega

4.05\text{ k}\Omega

50\text{ k}\Omega

20\text{ k}\Omega

Show answer & explanation

Answer: $50\text{ k}\Omega$

Answer

The required new resistance of the circuit is

50\text{ k}\Omega

.

According to Ohm's law, resistance equals voltage divided by current (

R = \frac{V}{I}

). Converting the target current of

9\text{ mA}

to standard amperes yields

0.009\text{ A}

. Dividing the constant source voltage of

450\text{ V}

by

0.009\text{ A}

results in

50,000\,\Omega

, which simplifies to

50\text{ k}\Omega

.

Step-by-Step Solution

1

Identify the target circuit parameters and convert metric units to base SI units

Voltage

V = 450\text{ V}

, Target Current

I = 9\text{ mA} = 9 \times 10^{-3}\text{ A} = 0.009\text{ A}

Ohm's law requires current to be in amperes when voltage is in volts to produce resistance in ohms.

2

Rearrange Ohm's law (

V = I \times R

) to solve for resistance (

R

)

R = \frac{V}{I}

Resistance is equal to the potential difference divided by the resulting current flow.

3

Calculate the target resistance and convert to kilohms

R = \frac{450\text{ V}}{0.009\text{ A}} = 50,000\,\Omega = 50\text{ k}\Omega

Dividing

450

by

0.009

gives

50,000\,\Omega

, which is expressed as

50\text{ k}\Omega

using standard metric prefixes.

Key Concept

Ohm's Law for Resistance (

R = \frac{V}{I}

) with Metric Prefix Conversion

Alternative Method

Using direct prefix arithmetic: since volts divided by milliamperes directly yields kilohms (

\frac{\text{V}}{\text{mA}} = \text{k}\Omega

), calculate

\frac{450\text{ V}}{9\text{ mA}} = 50\text{ k}\Omega

directly without manual decimal expansion.

Estimated Time:1m 15s

Question 6Question →

A technician is troubleshooting a $24 \text{ V}$ direct current (DC) control circuit. Currently, the circuit draws $8 \text{ mA}$ of current. In order to reduce the current draw to $2 \text{ mA}$ without changing the voltage source, how much additional resistance must be added in series to the existing circuit?

9 \text{ k}\Omega

12 \text{ k}\Omega

4 \text{ k}\Omega

9 \text{ }\Omega

Show answer & explanation

Answer: $9 \text{ k}\Omega$

Answer

The correct amount of additional resistance needed is

9 \text{ k}\Omega

.

To find the additional resistance required, first determine the current resistance (

R = \frac{24 \text{ V}}{0.008 \text{ A}} = 3 \text{ k}\Omega

). Next, calculate the total target resistance needed to limit the current to

2 \text{ mA}

(

R = \frac{24 \text{ V}}{0.002 \text{ A}} = 12 \text{ k}\Omega

). Finally, subtract the existing resistance from the target total to find the additional series resistance required (

12 \text{ k}\Omega - 3 \text{ k}\Omega = 9 \text{ k}\Omega

).

Step-by-Step Solution

1

Calculate the initial resistance of the circuit.

R_1 = \frac{24 \text{ V}}{0.008 \text{ A}} = 3,000 \text{ }\Omega

or

3 \text{ k}\Omega

Ohm's Law (

R = \frac{V}{I}

) is used to find the existing resistance before modifications.

2

Calculate the target total resistance required to limit the current to

2 \text{ mA}

.

R_2 = \frac{24 \text{ V}}{0.002 \text{ A}} = 12,000 \text{ }\Omega

or

12 \text{ k}\Omega

Ohm's Law is applied again to determine the total resistance needed for the new current requirement.

3

Determine the additional resistance needed by subtracting the initial resistance from the target total resistance.

12 \text{ k}\Omega - 3 \text{ k}\Omega = 9 \text{ k}\Omega

Resistors in series add together (

R_{total} = R_1 + R_{added}

). To find the added portion, subtract the existing resistance from the total.

Key Concept

Ohm's Law Calculations and Concepts

Question 7Question →

An industrial control panel supplies a constant $24\text{ V}$ DC to a sensor circuit. During normal operation, the sensor draws a current of $16\text{ mA}$ . Following a component degradation, the measured current rises to $64\text{ mA}$ at the same operating voltage. By how many ohms ( $\Omega$ ) has the circuit's total resistance decreased?

Show answer & explanation

Answer: 1125

Answer

The circuit's total resistance decreased by

1125\text{ }\Omega

.

According to Ohm's law, resistance equals voltage divided by current (

R = \frac{V}{I}

). Converting the currents to amperes gives

0.016\text{ A}

and

0.064\text{ A}

. The initial resistance is

R_1 = \frac{24\text{ V}}{0.016\text{ A}} = 1500\text{ }\Omega

, and the final resistance is

R_2 = \frac{24\text{ V}}{0.064\text{ A}} = 375\text{ }\Omega

. The decrease in resistance is

1500\text{ }\Omega - 375\text{ }\Omega = 1125\text{ }\Omega

.

Step-by-Step Solution

1

Convert current quantities from milliamperes (mA) to amperes (A)

I_1 = 0.016\text{ A}

and

I_2 = 0.064\text{ A}

Ohm's law requires current to be expressed in standard SI units (amperes) to yield resistance in ohms.

2

Calculate the initial resistance using Ohm's law (

R = \frac{V}{I}

)

R_1 = \frac{24\text{ V}}{0.016\text{ A}} = 1500\text{ }\Omega

Determines the baseline operating resistance of the sensor module.

3

Calculate the degraded state resistance using Ohm's law (

R = \frac{V}{I}

)

R_2 = \frac{24\text{ V}}{0.064\text{ A}} = 375\text{ }\Omega

Determines the lower operating resistance corresponding to the increased current draw.

4

Calculate the net difference between initial and degraded resistance

\Delta R = 1500\text{ }\Omega - 375\text{ }\Omega = 1125\text{ }\Omega

Finds the exact reduction in total circuit resistance.

Key Concept

Ohm's Law (

R = \frac{V}{I}

) applied to determine resistance changes in DC circuits with metric prefix conversion.

Estimated Time:1m 30s

Question 8Question →

A technician connects a $24\text{ V}$ direct current (DC) power source across an auxiliary heating element with a measured resistance of $8\text{ }\Omega$ . What is the amount of current flowing through the heating element?

192\text{ A}

0.33\text{ A}

3\text{ A}

24\text{ A}

Show answer & explanation

Answer: $3\text{ A}$

Answer

3\text{ A}

According to Ohm's law, current (

I

) is calculated by dividing voltage (

V

) by resistance (

R

). For a

24\text{ V}

supply connected across an

8\text{ }\Omega

load, the calculation is

I = \frac{24\text{ V}}{8\text{ }\Omega} = 3\text{ A}

.

Step-by-Step Solution

1

Identify the given values from the problem statement.

Voltage (

V

) =

24\text{ V}

, Resistance (

R

) =

8\text{ }\Omega

.

Ohm's law relates voltage, current, and resistance in a DC circuit.

2

Select the appropriate form of Ohm's law to solve for current (

I

).

I = \frac{V}{R}

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

3

Substitute the known values into the equation and compute the result.

I = \frac{24\text{ V}}{8\text{ }\Omega} = 3\text{ A}

Dividing

24

by

8

gives the circuit current in amperes.

Key Concept

Ohm's Law relationship between voltage, current, and resistance (

I = \frac{V}{R}

)

Estimated Time:45s

Question 9Question →

Match each electrical quantity from Ohm's law on the left with its correct algebraic formula on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Voltage (

V

) matches with

I \times R

, Current (

I

) matches with

\frac{V}{R}

, and Resistance (

R

) matches with

\frac{V}{I}

.

According to Ohm's law, voltage equals current multiplied by resistance (

V = IR

). Solving for current isolates

I

by dividing voltage by resistance (

I = \frac{V}{R}

), and solving for resistance isolates

R

by dividing voltage by current (

R = \frac{V}{I}

).

Step-by-Step Solution

1

Identify the base equation of Ohm's law that calculates potential difference.

V = I \times R

Ohm's law defines voltage as the product of current and resistance.

2

Rearrange the base formula to solve for current by isolating

I

.

I = \frac{V}{R}

Dividing both sides of the base formula by resistance isolates current.

3

Rearrange the base formula to solve for resistance by isolating

R

.

R = \frac{V}{I}

Dividing both sides of the base formula by current isolates resistance.

Key Concept

Ohm's Law algebraic variations (

V = IR

,

I = \frac{V}{R}

,

R = \frac{V}{I}

)

Estimated Time:45s

Question 10Question →

An automotive technician tests a $12\text{ V}$ direct current (DC) circuit powering an auxiliary cooling fan. If the multimeter measures a current of $3\text{ A}$ flowing through the fan motor, what is the electrical resistance of the motor?

36\text{ }\Omega

0.25\text{ }\Omega

4\text{ }\Omega

9\text{ }\Omega

Show answer & explanation

Answer: $4\text{ }\Omega$

Answer

4\text{ }\Omega

According to Ohm's law, resistance equals voltage divided by current (

R = \frac{V}{I}

). Dividing

12\text{ V}

by

3\text{ A}

yields

4\text{ }\Omega

.

Step-by-Step Solution

1

Identify the known values and target quantity from Ohm's law.

Voltage (

V

) =

12\text{ V}

, Current (

I

) =

3\text{ A}

, Resistance (

R

) = unknown.

Setting up the given parameters ensures the proper mathematical formula is selected.

2

Rearrange Ohm's law (

V = I \times R

) to solve for resistance (

R

).

R = \frac{V}{I}

Dividing both sides by current isolates resistance as the subject.

3

Substitute the measured values into the formula and calculate.

R = \frac{12\text{ V}}{3\text{ A}} = 4\text{ }\Omega

Carrying out the division gives the total electrical resistance of the fan motor.

Key Concept

Ohm's Law:

R = \frac{V}{I}

Estimated Time:45s

Question 11Question →

A technician connects a direct current (DC) indicator lamp across a $10\text{ V}$ power supply. A digital multimeter connected in series measures a current of $0.5\text{ A}$ flowing through the circuit. What is the electrical resistance of the indicator lamp in ohms ( $\Omega$ )?

Show answer & explanation

Answer: 20

Answer

The resistance of the indicator lamp is

20\text{ }\Omega

.

According to Ohm's Law, resistance is determined by dividing voltage by current (

R = \frac{V}{I}

). Substituting

10\text{ V}

and

0.5\text{ A}

gives

R = \frac{10\text{ V}}{0.5\text{ A}} = 20\text{ }\Omega

.

Step-by-Step Solution

1

Identify the given circuit parameters from the problem statement.

Voltage

V = 10\text{ V}

, Current

I = 0.5\text{ A}

Applying Ohm's law requires identifying the known electromotive force and circuit current.

2

Select and arrange the Ohm's law equation to solve for resistance (

R

).

R = \frac{V}{I}

Resistance is equal to the voltage divided by the current flowing through the component.

3

Substitute the measured values into the formula and solve.

R = \frac{10\text{ V}}{0.5\text{ A}} = 20\text{ }\Omega

Dividing

10\text{ V}

by

0.5\text{ A}

yields the total resistance of

20\text{ }\Omega

.

Key Concept

Ohm's Law defines the relationship between voltage, current, and resistance in an electrical circuit:

V = I \times R

, which rearranges to

R = \frac{V}{I}

.

Estimated Time:45s

Question 12Question →

A technician is testing a direct current (DC) relay coil connected to a $48\text{ V}$ power supply. An ammeter placed in series with the circuit measures a steady current of $150\text{ mA}$ . Based on Ohm's law, what is the internal electrical resistance of the relay coil in ohms ( $\Omega$ )?

Show answer & explanation

Answer: 320

Answer

The internal electrical resistance of the relay coil is

320\text{ }\Omega

.

According to Ohm's law, resistance is found by dividing voltage by current (

R = \frac{V}{I}

). Converting

150\text{ mA}

to

0.15\text{ A}

and dividing the applied voltage of

48\text{ V}

by

0.15\text{ A}

yields exactly

320\text{ }\Omega

.

Step-by-Step Solution

1

Convert the current measurement from milliamperes to base amperes

I = 150\text{ mA} = 150 \times 10^{-3}\text{ A} = 0.15\text{ A}

Standard electrical calculations using Ohm's law require current in amperes.

2

Rearrange Ohm's law formula (

V = I \times R

) to isolate resistance (

R

)

R = \frac{V}{I}

The circuit voltage and current are known, and resistance is the required unknown quantity.

3

Substitute the given voltage and converted current into the formula and solve

R = \frac{48\text{ V}}{0.15\text{ A}} = 320\text{ }\Omega

Dividing

48

by

0.15

(or multiplying

48 \times \frac{20}{3}

) computes the exact resistance value.

Key Concept

Ohm's law states that electrical resistance (

R

) is the ratio of voltage (

V

) across a component to the current (

I

) flowing through it:

R = \frac{V}{I}

.

Estimated Time:1m 0s

Question 13Question →

An electronics technician tests a direct current (DC) alarm buzzer with a measured resistance of $40\text{ }\Omega$ . If an ammeter connected in the circuit measures a current flow of $0.5\text{ A}$ , what is the voltage applied across the buzzer?

80\text{ V}

20\text{ V}

0.0125\text{ V}

20\text{ mV}

Show answer & explanation

Answer: $20\text{ V}$

Answer

20\text{ V}

According to Ohm's law, voltage across a component equals the current flowing through it multiplied by its resistance (

V = I \times R

). Multiplying

0.5\text{ A}

by

40\text{ }\Omega

gives exactly

20\text{ V}

.

Step-by-Step Solution

1

Identify the given values and unknown variable from the problem statement.

Current (

I

) =

0.5\text{ A}

, Resistance (

R

) =

40\text{ }\Omega

, Voltage (

V

) = ?

Establishing the known quantities determines which algebraic arrangement of Ohm's law is required.

2

Select and apply the standard Ohm's law formula for voltage.

V = I \times R

Voltage is equal to the product of current in amperes and resistance in ohms.

3

Substitute the given numerical values into the formula and calculate.

V = 0.5\text{ A} \times 40\text{ }\Omega = 20\text{ V}

Multiplying the decimal current by the integer resistance yields the total potential difference in volts.

Key Concept

Ohm's Law expresses the fundamental relationship between voltage, current, and resistance in a DC circuit (

V = I \times R

).

Estimated Time:45s

Question 14Question →

An avionics technician tests a $72\text{ V}$ direct current (DC) instrument circuit. If the circuit's total resistance is measured at $1.2\text{ k}\Omega$ , what is the current flowing through the circuit?

16.7\text{ mA}

60\text{ mA}

60\text{ A}

86.4\text{ A}

Show answer & explanation

Answer: $60\text{ mA}$

Answer

60\text{ mA}

According to Ohm's law, current equals voltage divided by resistance (

I = V / R

). Converting

1.2\text{ k}\Omega

to base units gives

1200\text{ }\Omega

. Dividing

72\text{ V}

by

1200\text{ }\Omega

produces

0.06\text{ A}

, which is equivalent to

60\text{ mA}

.

Step-by-Step Solution

1

Convert the given resistance from kilo-ohms to base ohms

R = 1.2\text{ k}\Omega = 1.2 \times 10^3\text{ }\Omega = 1200\text{ }\Omega

Standard electrical calculations using Ohm's law require values to be expressed in SI base units (volts, amperes, and ohms).

2

Apply Ohm's law formula to solve for current (

I

)

I = \frac{V}{R} = \frac{72\text{ V}}{1200\text{ }\Omega} = 0.06\text{ A}

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

3

Convert the current from amperes to milliamperes

I = 0.06\text{ A} \times 1000\text{ mA/A} = 60\text{ mA}

Expressing the small current value in milliamperes matches standard electronic measurement conventions.

Key Concept

Ohm's Law Current Calculation (

I = \frac{V}{R}

) with Metric Prefix Conversion

Alternative Method

Convert the calculation directly using milliamperes:

1\text{ V} / 1\text{ k}\Omega = 1\text{ mA}

. Therefore,

72\text{ V} / 1.2\text{ k}\Omega = 60\text{ mA}

.

Estimated Time:1m 0s

Question 15Question →

Match each circuit modification on the left with its resulting effect on circuit current according to Ohm's law on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Doubling voltage with constant resistance doubles current; doubling resistance with constant voltage halves current; doubling both voltage and resistance keeps current unchanged; halving voltage while doubling resistance reduces current to one-fourth.

Ohm's law states

I = \frac{V}{R}

. Analyzing each case:

V \times 2 \implies I \times 2

;

R \times 2 \implies I \times 0.5

; both

\times 2 \implies I \times 1

; and

V \times 0.5

combined with

R \times 2 \implies I \times 0.25

.

Step-by-Step Solution

1

Recall Ohm's law relating current, voltage, and resistance

I = \frac{V}{R}

Current equals voltage divided by resistance.

2

Apply proportional reasoning for each condition

Direct proportionality for voltage, inverse proportionality for resistance.

Changes in numerator directly multiply the result, while changes in denominator inversely divide the result.

Key Concept

Ohm's law governs the relationship between voltage, current, and resistance (

I = \frac{V}{R}

), establishing that current is directly proportional to voltage and inversely proportional to resistance.

Estimated Time:45s

Question 16Question →

A direct current (DC) heating element is connected to a $120\text{ V}$ power supply. If an ammeter measures a current of $4\text{ A}$ flowing through the element, what is its electrical resistance?

480\text{ }\Omega

30\text{ }\Omega

0.033\text{ }\Omega

116\text{ }\Omega

Show answer & explanation

Answer: $30\text{ }\Omega$

Answer

30\text{ }\Omega

According to Ohm's law, electrical resistance (

R

) is defined as the ratio of voltage (

V

) across a component to the current (

I

) passing through it:

R = \frac{V}{I}

. Substituting

120\text{ V}

and

4\text{ A}

gives

R = \frac{120}{4} = 30\text{ }\Omega

.

Step-by-Step Solution

1

Identify the given values and the required quantity

Voltage

V = 120\text{ V}

, Current

I = 4\text{ A}

, Resistance

R

is unknown

Establishing the known circuit parameters determines which Ohm's law formula variation to use.

2

Apply Ohm's law rearranged to solve for resistance:

R = \frac{V}{I}

R = \frac{120\text{ V}}{4\text{ A}} = 30\text{ }\Omega

Resistance represents the opposition to current flow and is calculated as the ratio of electromotive force to electrical current.

Key Concept

Ohm's Law Resistance Calculation (

R = \frac{V}{I}

)

Estimated Time:45s

Question 17Question →

Match each direct current (DC) circuit scenario on the left with its corresponding calculated electrical quantity on the right using Ohm's law ( $V = I \times R$ ).

Click a left item, then click its matching right item

Show answer & explanation

Answer

The

120\text{ V}

load with

2.4\text{ k}\Omega

matches the resulting current of

50\text{ mA}

; the

5\text{ V}

circuit drawing

20\text{ mA}

matches the circuit resistance of

250\text{ }\Omega

; the

400\text{ mA}

current through

50\text{ }\Omega

matches the voltage drop of

20\text{ V}

; and the

36\text{ V}

loop carrying

3\text{ mA}

matches the loop resistance of

12\text{ k}\Omega

.

Each circuit condition correctly maps to its target electrical parameter by converting metric prefixes (

1\text{ k}\Omega = 1000\text{ }\Omega

,

1\text{ mA} = 0.001\text{ A}

) and applying the appropriate algebraic form of Ohm's law:

I = \frac{V}{R}

,

R = \frac{V}{I}

, and

V = I \times R

.

Step-by-Step Solution

1

Calculate current for the

120\text{ V}

,

2.4\text{ k}\Omega

circuit

I = \frac{120\text{ V}}{2400\text{ }\Omega} = 0.05\text{ A} = 50\text{ mA}

Ohm's law states

I = \frac{V}{R}

, requiring resistance in fundamental ohms (

1\text{ k}\Omega = 1000\text{ }\Omega

).

2

Calculate resistance for the

5\text{ V}

,

20\text{ mA}

circuit branch

R = \frac{5\text{ V}}{0.02\text{ A}} = 250\text{ }\Omega

Rearranging Ohm's law gives

R = \frac{V}{I}

, requiring current in amperes (

20\text{ mA} = 0.02\text{ A}

).

3

Calculate voltage drop across the

50\text{ }\Omega

element carrying

400\text{ mA}

V = 0.4\text{ A} \times 50\text{ }\Omega = 20\text{ V}

Ohm's law formula

V = I \times R

computes potential difference when current and resistance are known.

4

Calculate total resistance for the

36\text{ V}

,

3\text{ mA}

sensor loop

R = \frac{36\text{ V}}{0.003\text{ A}} = 12000\text{ }\Omega = 12\text{ k}\Omega

Applying

R = \frac{V}{I}

with

3\text{ mA} = 0.003\text{ A}

yields

12000\text{ }\Omega

, or

12\text{ k}\Omega

.

Key Concept

Ohm's law mathematically relates voltage (

V

), current (

I

), and resistance (

R

) via

V = I \times R

,

I = \frac{V}{R}

, and

R = \frac{V}{I}

, requiring consistent base metric units.

Estimated Time:1m 15s

Question 18Question →

A direct current (DC) solenoid valve in an industrial pneumatic system has an internal coil resistance of $15\text{ }\Omega$ . When connected to a $30\text{ V}$ DC power supply, what is the current flowing through the solenoid coil in amperes ( $\text{A}$ )?

Show answer & explanation

Answer: 2

Answer

The current flowing through the solenoid coil is

2\text{ A}

.

According to Ohm's law, electrical current (

I

) equals voltage (

V

) divided by resistance (

R

). Substituting the given values yields

I = \frac{30\text{ V}}{15\text{ }\Omega} = 2\text{ A}

.

Step-by-Step Solution

1

Identify the given circuit parameters

Voltage

V = 30\text{ V}

, Resistance

R = 15\text{ }\Omega

Extract the given values to identify which Ohm's law formula variation is required.

2

State Ohm's law formula for current

I = \frac{V}{R}

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

3

Substitute the values and evaluate

I = \frac{30\text{ V}}{15\text{ }\Omega} = 2\text{ A}

Dividing

30

by

15

yields the circuit current in amperes.

Key Concept

Ohm's Law (

I = \frac{V}{R}

)

Estimated Time:45s

Question 19Question →

A direct current (DC) emergency lighting circuit operates from a $28\text{ V}$ power supply. An in-line ammeter measures a steady current flow of $350\text{ mA}$ through the circuit. What is the total electrical resistance of the lighting circuit?

0.08\text{ }\Omega

9.8\text{ }\Omega

12.5\text{ }\Omega

80\text{ }\Omega

Show answer & explanation

Answer: $80\text{ }\Omega$

Answer

The total electrical resistance of the lighting circuit is

80\text{ }\Omega

.

According to Ohm's law, resistance is found by dividing voltage by current (

R = V / I

). Converting

350\text{ mA}

into amperes yields

0.35\text{ A}

. Dividing

28\text{ V}

by

0.35\text{ A}

gives the correct value of

80\text{ }\Omega

.

Step-by-Step Solution

1

Convert the current measurement from milliamperes to amperes.

I = 350\text{ mA} = \frac{350}{1000}\text{ A} = 0.35\text{ A}

Standard Ohm's law calculations require current to be in base SI units (amperes) to produce resistance in ohms.

2

Rearrange Ohm's law (

V = I \times R

) to solve for resistance (

R

).

R = \frac{V}{I}

Resistance equals the electromotive force (voltage) across the circuit divided by the resulting current flow.

3

Substitute the known voltage and converted current values into the rearranged formula.

R = \frac{28\text{ V}}{0.35\text{ A}} = \frac{2800}{35}\text{ }\Omega = 80\text{ }\Omega

Dividing

28\text{ V}

by

0.35\text{ A}

determines the load resistance in ohms.

Key Concept

Ohm's Law (

V = I \times R

) defines the mathematical relationship between voltage, current, and resistance in DC circuits, requiring proper metric unit conversion before calculation.

Estimated Time:1m 0s

Question 20Question →

An electronics technician tests a DC audio indicator module connected to a $24\text{ V}$ power supply. An in-line meter measures a steady current flow of $80\text{ mA}$ through the component. According to Ohm's law, what is the electrical resistance of the module in ohms ( $\Omega$ )?

Show answer & explanation

Answer: 300

Answer

The total resistance of the module is

300\text{ }\Omega

.

According to Ohm's law (

V = I \times R

), resistance equals voltage divided by current (

R = \frac{V}{I}

). Converting

80\text{ mA}

to standard amperes gives

0.08\text{ A}

. Dividing the

24\text{ V}

source by

0.08\text{ A}

yields a resistance of

300\text{ }\Omega

.

Step-by-Step Solution

1

Convert current from milliamperes (mA) to base amperes (A)

80\text{ mA} = 80 \times 10^{-3}\text{ A} = 0.08\text{ A}

Ohm's law requires current to be expressed in standard SI units (amperes) when working with volts and ohms.

2

Rearrange Ohm's law (

V = I \times R

) to isolate resistance (

R

)

R = \frac{V}{I}

Dividing both sides of the standard Ohm's law equation by current isolates the unknown resistance.

3

Substitute the known voltage (

24\text{ V}

) and current (

0.08\text{ A}

) into the formula

R = \frac{24\text{ V}}{0.08\text{ A}} = 300\text{ }\Omega

Performing the division calculates the exact resistance value in ohms.

Key Concept

Ohm's law resistance calculation with metric prefix conversion (

R = \frac{V}{I}

)

Estimated Time:1m 0s

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