In the given figure,the value of resistance X | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) The potential difference between $B$ and $D$ is zero,which means the Wheatstone bridge is in a balanced condition.For a balanced Wheatstone bridge

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(C) The potential difference between $B$ and $D$ is zero,which means the Wheatstone bridge is in a balanced condition.For a balanced Wheatstone bridge,the ratio of resistances in the arms must be equal:$\frac{R_{AB}}{R_{BC}} = \frac{R_{AD}}{R_{DC}}$First,calculate the equivalent resistances of the arms:$R_{AB} = 15 + 6 = 21 \, \Omega$$R_{BC} = 3 + \frac{8X}{8 + X} \, \Omega$$R_{AD} = 15 + (6 || 6) = 15 + 3 = 18 \, \Omega$$R_{DC} = 4 + (4 || 4) = 4 + 2 = 6 \, \Omega$Now,apply the balanced condition:$\frac{21}{3 + \frac{8X}{8 + X}} = \frac{18}{6}$$\frac{21}{3 + \frac{8X}{8 + X}} = 3$$7 = 3 + \frac{8X}{8 + X}$$4 = \frac{8X}{8 + X}$$4(8 + X) = 8X$$32 + 4X = 8X$$4X = 32$$X = 8 \, \Omega$

In the given figure,the value of resistance $X$ will be,when the potential difference between $B$ and $D$ is zero. (in $\Omega$)

Similar Questions

What are the uses of a Wheatstone bridge?

The figure shows a network of five resistances and two batteries. The current through the $30\,V$ battery is ............... $A$.

Kirchhoff's first law $(\Sigma i = 0)$ and second law $(\Sigma iR = \Sigma E)$ are based on which of the following respectively? (Where the symbols have their usual meanings.)

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

The current through the wire $XY$ of the circuit shown is ................ $A$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module