Two wires A and B of equal lengths are connected in left and right gap of a meter bridge, null point is obtained at 40 cm from left end. Diameters of the wire A and B are in that ratio 3: 1. The ratio of specific resistance of A to the of B is (a) 4: 1 (b) 3: 1 (c) 6: 1 (d) 8: 1

Answer: (c). Balance: (RA)/(RB) = 40/60 = 2/3. R = (ρ L)/(π d²/4) with equal L, so (ρA)/(ρB) = (RA)/(RB)((dA)/(dB))². (ρA)/(ρB) = 2/3 × 9 = 6. So the answer is (c) 6: 1.

Two wires A and B of equal lengths are connected in left and right… | MHT CET 2020 (16 Oct, Shift 1)

Q62MHT CET 2020 · 16 OCT · SHIFT 1Medium

Wheatstone Bridge & Metre Bridge

Two wires $A$ and $B$ of equal lengths are connected in left and right gap of a meter bridge, null point is obtained at $40\text{ cm}$ from left end. Diameters of the wire $A$ and $B$ are in that ratio $3 : 1$ . The ratio of specific resistance of $A$ to the of $B$ is

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Answer: (c)

Balance: $\dfrac{R_A}{R_B} = \dfrac{40}{60} = \dfrac{2}{3}$ .
$R = \dfrac{\rho L}{\pi d^2/4}$ with equal $L$ , so $\dfrac{\rho_A}{\rho_B} = \dfrac{R_A}{R_B}\left(\dfrac{d_A}{d_B}\right)^2$ .
$\dfrac{\rho_A}{\rho_B} = \dfrac{2}{3} \times 9 = 6$ .
So the answer is (c) $6 : 1$ .

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Wheatstone Bridge & Metre Bridge question from MHT CET 2020 (16 Oct, Shift 1)

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