An aircraft cockpit lighting circuit is connected to a 24\text{ V} direct current (DC) pow… — Armed Services Vocational Aptitude Battery (ASVAB)

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?

Answer: 10 V

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

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.

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.

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

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