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In a Wheatstone bridge, resistors R1 and R2 occupy two adjacent arms while capacitors C1 and C2 occupy the other two adjacent arms. When a key is pressed the galvanometer shows no deflection. Which of the following expressions correctly represents the balance condition for this bridge?

1. R1/R2 = C1/C2
2. R1/R2 = C2/C1
3. R1/(R1 + R2) = C2/(C1 - C2)
4. R1/(R1 - R2) = C2/(C1 + C2)

Correct answer: R1/R2 = C2/C1

Solution

For balance, the ratio of impedances in the two arms must be equal: R1/R2 = Z_C1/Z_C2 = (1/C1)/(1/C2) = C2/C1. This is a well-known result for a bridge with two resistive and two capacitive arms.

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