(B) The balancing condition for a Wheatstone's bridge is $\frac{P}{Q} = \frac{R_3}{R_4}$,where $R_3$ is the resistance in the third arm and $R_4$ is t

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(B) The balancing condition for a Wheatstone's bridge is $\frac{P}{Q} = \frac{R_3}{R_4}$,where $R_3$ is the resistance in the third arm and $R_4$ is the resistance in the fourth arm $(S)$.Given $R_3 = 625\, \Omega$ and $R_4 = S$,we have:$\frac{P}{Q} = \frac{625}{S}$ ..................... $(1)$When $P$ and $Q$ are interchanged,the new resistance in the third arm becomes $625 + 51 = 676\, \Omega$. The bridge is balanced again,so:$\frac{Q}{P} = \frac{676}{S}$$\frac{P}{Q} = \frac{S}{676}$ ..................... $(2)$Equating $(1)$ and $(2)$:$\frac{625}{S} = \frac{S}{676}$$S^2 = 625 \times 676$$S = \sqrt{625} \times \sqrt{676} = 25 \times 26 = 650\, \Omega$.

Class 12 Physics Current Electricity Kirchhoff's Law and Whitestone Bridge Circuit solving

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$A$ Wheatstone's bridge is balanced with a resistance of $625\, \Omega$ in the third arm,where $P, Q$ and $S$ are in the $1^{st}, 2^{nd}$ and $4^{th}$ arm respectively. If $P$ and $Q$ are interchanged,the resistance in the third arm has to be increased by $51\,\Omega$ to secure balance. The unknown resistance in the fourth arm is ............. $\Omega$.

A
$625$
B
$650$
C
$676$
D
$600$

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Current Electricity

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Kirchhoff's Law and Whitestone Bridge Circuit solving

In a Wheatstone bridge,three resistors $P$,$Q$,and $R$ are connected in three arms,and the fourth arm is formed by the parallel combination of two resistors $S_1$ and $S_2$. The condition for the bridge to be balanced is:

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Five equal resistances are connected in a network as shown in the figure. The net resistance between the points $A$ and $B$ is

MediumJEE MAIN 2021

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The Wheatstone bridge principle is used to measure the specific resistance $(S_1)$ of a given wire,having length $L$ and radius $r$. If $X$ is the resistance of the wire,then the specific resistance is: $S_1 = X \left( \frac{\pi r^2}{L} \right)$. If the length of the wire is doubled,then the value of the specific resistance will be:

DifficultJEE MAIN 2024

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In a Wheatstone bridge (see figure),resistances $P$ and $Q$ are approximately equal. When $R = 400 \,\Omega$,the bridge is balanced. On interchanging $P$ and $Q$,the value of $R$ for balance is $405 \,\Omega$. The value of $X$ is close to ................. $\Omega$. (in $.5$)

MediumJEE MAIN 2019

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$A$ Wheatstone bridge is initially at room temperature and all arms of the bridge have the same value of resistance $(R_1=R_2=R_3=R_4=R)$. When $R_3$ is heated to some temperature, its resistance value increases by $10 \%$. The potential difference $(V_a - V_b)$ (after $R_3$ is heated) is . . . . . . $V$. Given the total voltage is $40 \text{ V}$.

DifficultJEE MAIN 2026

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In a Wheatstone bridge,three resistors $P$,$Q$,and $R$ are connected in three arms,and the fourth arm is formed by the parallel combination of two resistors $S_1$ and $S_2$. The condition for the bridge to be balanced is:

Five equal resistances are connected in a network as shown in the figure. The net resistance between the points $A$ and $B$ is

In a Wheatstone bridge (see figure),resistances $P$ and $Q$ are approximately equal. When $R = 400 \,\Omega$,the bridge is balanced. On interchanging $P$ and $Q$,the value of $R$ for balance is $405 \,\Omega$. The value of $X$ is close to ................. $\Omega$. (in $.5$)

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