If the potential difference between points B | vedclass

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Question

(A) The given circuit is a Wheatstone bridge. Let the top node be $A$ and the bottom node be $C$. The potential difference between $B$ and $D$ is zero

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(A) The given circuit is a Wheatstone bridge. Let the top node be $A$ and the bottom node be $C$. The potential difference between $B$ and $D$ is zero, which means the bridge is balanced.In a balanced Wheatstone bridge, the ratio of resistances in the opposite arms is equal.Let $R_1$ be the equivalent resistance of the parallel combination of $6 	ext{ } \Omega$ and $3 	ext{ } \Omega$ resistors: $R_1 = (6 	imes 3) / (6 + 3) = 18 / 9 = 2 	ext{ } \Omega$.Let $R_2$ be the equivalent resistance of the parallel combination of $x 	ext{ } \Omega$ and $1 	ext{ } \Omega$ resistors: $R_2 = (x 	imes 1) / (x + 1) = x / (x + 1) 	ext{ } \Omega$.Let $R_3$ be the series combination of $1 	ext{ } \Omega$ and $2 	ext{ } \Omega$ resistors: $R_3 = 1 + 2 = 3 	ext{ } \Omega$.Let $R_4$ be the resistance $x 	ext{ } \Omega$.For a balanced bridge, $R_1 / R_3 = R_2 / R_4$.Substituting the values: $2 / 3 = [x / (x + 1)] / x$.$2 / 3 = 1 / (x + 1)$.$2(x + 1) = 3$.$2x + 2 = 3$.$2x = 1$.$x = 1/2 	ext{ } \Omega$.Comparing $x = 1/2 	ext{ } \Omega$ with $x = 1/n 	ext{ } \Omega$, we get $n = 2$.

If the potential difference between points $B$ and $D$ is zero in the given circuit, the value of $x$ is $1/n \text{ } \Omega$. The value $n$ is

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