A 50 $\mathrm { k } \Omega$ potentiometer is connected across a 15 V source. If the voltage from the wiper to the lower end of the potentiometer is 3.2 V , what is the resistance of that lower part?
A) 39.3 $\mathrm { k } \Omega$
B) 50 $\mathrm { k } \Omega$
C) 10.7 $\mathrm { k } \Omega$
D) 0

Question

A 50 $\mathrm { k } \Omega$ potentiometer is connected across a  15 V  source. If the voltage from the wiper to the lower end of the potentiometer is  3.2 V , what is the resistance of that lower part?
A) 39.3 $\mathrm { k } \Omega$ 
B) 50 $\mathrm { k } \Omega$ 
C) 10.7 $\mathrm { k } \Omega$ 
D) 0

Quizplus · Accepted Answer

Since the voltage from the wiper to the lower end of the potentiometer is 3.2 V, the voltage from the wiper to the upper end of the potentiometer is 15 V - 3.2 V = 11.8 V. Using the voltage divider formula, we can find the ratio of the lower part (R) to the total resistance (50 $\mathrm { k } \Omega$):
$$
\frac{R}{R+50k\Omega}=\frac{3.2V}{15V-3.2V}=0.253
$$
Solving for R gives:
$$
R=0.253\times50\mathrm{k}\Omega=12.65\mathrm{k}\Omega
$$
Therefore, the lower part has a resistance of 10.7 kΩ (closest option is C).

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A 50 $\mathrm { k } \Omega$ Potentiometer Is Connected Across a 15 V Source