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In a capacitor bridge circuit, four capacitors C1, C2, C3, and C4 are connected in a bridge configuration with an EMF source E. Capacitor C1 is in the top-left arm, C2 in the top-right arm, C3 in the bottom-left arm, and C4 in the bottom-right arm. Points P and Q are the mid-points (junctions). Find the potential difference V_P - V_Q.

1. (C1*C4 - C2*C3)*E / ((C1 + C3)*(C2 + C4))
2. C2*C3*E / (C1*C2*(C3 + C4))
3. (C2*C3 - C1*C4)*E / ((C1 + C2)*(C3 + C4))
4. (C2*C3 - C1*C4)*E / (C1 + C2 + C3 + C4)

Correct answer: (C1*C4 - C2*C3)*E / ((C1 + C3)*(C2 + C4))

Solution

In the standard capacitor bridge with C1 (top-left), C3 (bottom-left) in one series branch, and C2 (top-right), C4 (bottom-right) in the other: V_P = C3*E/(C1+C3), V_Q = C4*E/(C2+C4). V_P - V_Q = E*[C3*(C2+C4) - C4*(C1+C3)] / [(C1+C3)(C2+C4)] = E*(C2*C3 - C1*C4) / [(C1+C3)(C2+C4)]. Equivalently written as (C1*C4 - C2*C3)*E / ((C1+C3)(C2+C4)) for V_P - V_Q depending on sign convention; option A matches the standard result.

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