A 100\text{ k}\Omega linear potentiometer is connected across a 12\text{ V} DC power suppl… — Armed Services Vocational Aptitude Battery (ASVAB)

A $100\text{ k}\Omega$ linear potentiometer is connected across a $12\text{ V}$ DC power supply, with terminal 1 connected to $+12\text{ V}$ , terminal 3 connected to ground ( $0\text{ V}$ ), and terminal 2 serving as the adjustable wiper. If the wiper is set to $40\%$ of its total travel distance away from terminal 3 toward terminal 1, what is the output voltage measured at terminal 2 relative to ground, and what is the resistance between terminal 1 and terminal 2?

A
$7.2\text{ V}$ and $40\text{ k}\Omega$
$4.8\text{ V}$ and $60\text{ k}\Omega$ Answer
C
$4.8\text{ V}$ and $40\text{ k}\Omega$
D
$4.8\text{ V}$ and $600\ \Omega$

Answer

4.8\text{ V}

output voltage and

60\text{ k}\Omega

resistance between terminal 1 and terminal 2

A linear potentiometer configured across a DC voltage source acts as a continuous voltage divider. With terminal 3 connected to ground (

0\text{ V}

) and the wiper at

40\%

travel from ground, the lower resistance segment

R_{2-3}

40\text{ k}\Omega

, yielding an output voltage of

V_{\text{out}} = 12\text{ V} \times (40\text{ k}\Omega / 100\text{ k}\Omega) = 4.8\text{ V}

. The upper resistance segment between terminal 1 (

+12\text{ V}

) and terminal 2 (wiper) is the remaining portion:

100\text{ k}\Omega - 40\text{ k}\Omega = 60\text{ k}\Omega

Step-by-Step Solution

Calculate the resistance of the lower track section between terminal 2 (wiper) and terminal 3 (ground).

R_{2-3} = 0.40 \times 100\text{ k}\Omega = 40\text{ k}\Omega

The wiper is positioned at

40\%

of total travel measured from the ground terminal.

Calculate the output voltage

V_{\text{out}}

at terminal 2 relative to ground using the voltage divider relationship.

V_{\text{out}} = V_{\text{in}} \times \left(\frac{R_{2-3}}{R_{\text{total}}}\right) = 12\text{ V} \times \left(\frac{40\text{ k}\Omega}{100\text{ k}\Omega}\right) = 4.8\text{ V}

A potentiometer connected across a voltage source functions as an adjustable voltage divider.

Determine the remaining resistance between terminal 1 (

+12\text{ V}

) and terminal 2 (wiper).

R_{1-2} = R_{\text{total}} - R_{2-3} = 100\text{ k}\Omega - 40\text{ k}\Omega = 60\text{ k}\Omega

The total resistance is divided into two series segments by the wiper contact.

Key Concept

Potentiometer voltage division and wiper segment resistance distribution

Estimated Time:45s

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