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Four resistive wires A, B, C, and D each of length l = 10 cm and cross-sectional area 0.1 m² are connected in a Wheatstone-bridge type circuit. The resistivities are: rho_A = 1 ohm-m, rho_B = 3 ohm-m, rho_C = 6 ohm-m, rho_D = 1 ohm-m. Two switches S1 and S2 are present in the circuit. What is the position of the null point in the galvanometer arm?

1. Mid-point of wire B or wire C when both switches S1 and S2 are open
2. Mid-point of wire B when both switches S1 and S2 are closed
3. Mid-point of wire D when both switches S1 and S2 are open
4. None of these

Correct answer: None of these

Solution

The null point in a Wheatstone bridge occurs when P/Q = R/S. Here the ratios do not match with any simple mid-point position on any single wire, so none of the listed simple mid-point statements is correct. The question as stated relies on a specific circuit diagram not provided, making the precise answer circuit-dependent. Given the resistances R_A=1, R_B=3, R_C=6, R_D=1 ohm, the bridge is unbalanced and the answer is 'None of these'.

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