A 36\text{ V} DC power supply is connected across a series circuit containing a fixed 16\ … — Armed Services Vocational Aptitude Battery (ASVAB)

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?

A
$24\ \Omega$
$8\ \Omega$ Answer
C
$54\ \Omega$
D
$9.6\ \Omega$

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

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.

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

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