A rotary potentiometer has a total resistance of 50\text{ k}\Omega across its two outer fi… — Armed Services Vocational Aptitude Battery (ASVAB)

A rotary potentiometer has a total resistance of $50\text{ k}\Omega$ across its two outer fixed terminals (Terminals A and C). If the center wiper (Terminal B) is adjusted so that the resistance between Terminal A and Terminal B is $32\text{ k}\Omega$ , what is the resistance between Terminal B and Terminal C?

A
$32\text{ k}\Omega$
$18\text{ k}\Omega$ Answer
C
$82\text{ k}\Omega$
D
$1.8\text{ k}\Omega$

Answer

The resistance between Terminal B and Terminal C is

18\text{ k}\Omega

A potentiometer contains a single continuous resistive track between its two outer terminals (

A

and

C

). The center wiper (

B

) contacts this track at an intermediate point, splitting the total resistance into two complementary series sections such that

R_{AC} = R_{AB} + R_{BC}

. Given a total resistance of

50\text{ k}\Omega

and a segment of

32\text{ k}\Omega

, the remaining segment between the wiper and the other outer terminal must be

50\text{ k}\Omega - 32\text{ k}\Omega = 18\text{ k}\Omega

Step-by-Step Solution

Identify the relationship between the three terminals of a potentiometer.

The total resistance between outer terminals A and C equals the sum of the two sub-segments created by wiper B:

R_{AC} = R_{AB} + R_{BC}

A potentiometer consists of a single continuous resistive element where the movable wiper divides the total track into two series-connected resistive portions.

Subtract the known segment resistance from the total end-to-end resistance to find

R_{BC}

R_{BC} = 50\text{ k}\Omega - 32\text{ k}\Omega = 18\text{ k}\Omega

Isolating

R_{BC}

algebraically provides the remaining resistance along the element to the opposite outer terminal.

Key Concept

Potentiometer resistive track division

Estimated Time:45s

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