For what value of unknown resistance X,the po | vedclass

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(B) The circuit represents a Wheatstone bridge. The potential difference between $B$ and $D$ is zero when the bridge is balanced.For a balanced Wheats

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$6 \, \Omega$

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(B) The circuit represents a Wheatstone bridge. The potential difference between $B$ and $D$ is zero when the bridge is balanced.For a balanced Wheatstone bridge,the ratio of resistances in opposite arms must be equal: $\frac{R_{AB}}{R_{AD}} = \frac{R_{BC}}{R_{DC}}$.Here,$R_{AB} = 12 \, \Omega$.$R_{AD} = X + 6 \, \Omega$.$R_{BC}$ consists of two $1 \, \Omega$ resistors in parallel,so $R_{BC} = \frac{1 	imes 1}{1 + 1} = 0.5 \, \Omega$.$R_{DC}$ consists of two $1 \, \Omega$ resistors in parallel,so $R_{DC} = \frac{1 	imes 1}{1 + 1} = 0.5 \, \Omega$.Applying the balance condition: $\frac{12}{X + 6} = \frac{0.5}{0.5}$.$\frac{12}{X + 6} = 1$.$12 = X + 6$.$X = 6 \, \Omega$.

For what value of unknown resistance $X$,the potential difference between $B$ and $D$ will be zero in the circuit shown in the figure?

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