The resultant resistance between points B and | vedclass

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(C) The circuit is a Wheatstone bridge. Let the points be $A, B, C, D$ as shown in the figure. The resistance between $B$ and $D$ is to be calculated.

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(C) The circuit is a Wheatstone bridge. Let the points be $A, B, C, D$ as shown in the figure. The resistance between $B$ and $D$ is to be calculated.Here,the resistors are arranged such that the ratio of resistances in the arms is $\frac{R_{AB}}{R_{AD}} = \frac{3 \Omega}{3 \Omega} = 1$ and $\frac{R_{BC}}{R_{CD}} = \frac{3 \Omega}{3 \Omega} = 1$.Since the ratio is equal,the bridge is balanced. Therefore,no current flows through the central $6 \Omega$ resistor connected between $A$ and $C$.We can remove the $6 \Omega$ resistor from the circuit.Now,the circuit consists of two branches in parallel: one branch with two $3 \Omega$ resistors in series $(3+3 = 6 \Omega)$ and another branch with two $3 \Omega$ resistors in series $(3+3 = 6 \Omega)$.The equivalent resistance $R_{eq}$ between $B$ and $D$ is given by the parallel combination of these two $6 \Omega$ branches:$R_{eq} = \frac{6 \Omega 	imes 6 \Omega}{6 \Omega + 6 \Omega} = \frac{36}{12} = 3 \Omega$.

The resultant resistance between points $B$ and $D$ in the given figure is: (in $\Omega$)

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