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Question:

A potentiometer PQ is set up to compare two resistances as shown in the figure. The ammeter A in the circuit reads 1.0 A when two-way key K3 is open. The balance point is at a length l1 cm from P when two-way key K3 is plugged between 2 and 1, while the balance point is at a length l2 cm from P when key K3 is plugged between 3 and 1. What is the ratio of the two resistances R1/R2?

l1/(l1+l2)

l1/(l2-l1)

l1/(l1-l2)

l2/(l2-l1)

Solution:

When the key is at point (2), V1 = IR1 = xl1
When the key is at point (3), V2 = I(R1 + R2) = xl2
Therefore, R1/(R1 + R2) = l1/l2
R1l2 = l1(R1 + R2)
R1l2 = l1R1 + l1R2
R1l2 - l1R1 = l1R2
R1(l2 - l1) = l1R2
R1/R2 = l1/(l2 - l1)