A surveillance camera heating assembly is powered by a 120\text{ V} DC power supply connec… — Armed Services Vocational Aptitude Battery (ASVAB)

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 ( $R_2$ )?

A
$120\text{ V}$
$33\text{ V}$ Answer
C
$40\text{ V}$
D
$1.5\text{ V}$

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

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.

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.

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

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