The four arms of a Wheatstone bridge have resistances as shown in the… | JEE Main 2021 (17 Mar, Shift 2)

Q60JEE Main 2021 · 17 MAR · SHIFT 2Difficult

Wheatstone Bridge & Metre Bridge

The four arms of a Wheatstone bridge have resistances as shown in the figure. A galvanometer of 15 $\Omega$ resistance is connected across BD. Calculate the current through the galvanometer when a potential difference of 10V is maintained across AC.

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Answer: (b)

Let $I$ = cell current, $I_1$ in AB, $I_g$ in BD. Loop ABDA: $100I_1 + 15I_g - 60(I - I_1) = 0$ .
Loop BCDB: $10(I_1 - I_g) - 15I_g - 5(I - I_1 + I_g) = 0 \Rightarrow I = 3I_1 - 6I_g$ .
Substituting: $-20I_1 + 375I_g = 0 \Rightarrow I_1 = 18.75I_g$ , $I = 50.25I_g$ .
Loop ADC with cell: $60(I - I_1) + 5(I - I_1 + I_g) = 10 \Rightarrow 2052.5\,I_g = 10$ .
$I_g = 4.87 \times 10^{-3}\text{ A}$ . So the answer is (b) 4.87 mA.

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