$A$ 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 ............. $\Omega$
Diffcult
Download our app for free and get started
The balancing condition for Wheatstone's bridge is, $\frac{P}{Q}=\frac{S}{R}$
$\frac{P}{Q}=\frac{625}{R}$$.....................(1)$
When $\mathrm{P}$ and $\mathrm{Q}$ are interchanged we get,
$\frac{Q}{P}=\frac{676}{R}$
$\frac{P}{Q}=\frac{R}{676}$$.....................(2)$
Equating both the equations,
$\frac{P}{Q}=\frac{625}{R}=\frac{R}{676}$
$R^{2}=\sqrt{422500}$
$R=650 \Omega$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1In the fig. shown for given values of $R_1$ and $R_2$ the balance point for jockey is at $40\, cm$ from $A$. When $R_2$ is shunted by a resistance of $10\,\Omega $, balance shifts to $50\, cm. R_1$ and $R_2$ are $(AB = 1\,m)$View Solution
- 2The specific resistance of a wire is $\rho $, its volume is $3\,{m^3}$ and its resistance is $3\, ohms$, then its length will beView Solution
- 3If two bulbs of wattage $25$ and $30$, each rated at $220\, volts$, are connected in series with a $440$ $volt$ supply, which bulb will fuseView Solution
- 4Two cells of $e.m.f.$ $E_1$ and $E_2$ are joined in series and the balancing length of the potentiometer wire is $625$ $cm$. If the terminals of $E_1$ are reversed, the balancing length obtained is $125 \,cm$. Given $E_2 > E_1$, the ratio $E_1: E_2$ will beView Solution
- 5Current density in a cylindrical wire of radius $R$ is given as $J =$ $\left\{ {\begin{array}{*{20}{c}}View Solution
{{J_0}\left( {\frac{x}{R} - 1} \right)\,\,for\,\,0 \leqslant x < \frac{R}{2}} \\
{{J_0}\frac{x}{R}\,\,\,\,for\,\,\,\frac{R}{2} \leqslant x \leqslant R}
\end{array}} \right.$The current flowing in the wire is: - 6A filament bulb $(500 \,W,\,\, 100 \,V)$ is to be used in a $230\, V$ main supply. When a resistance $R$ is connected in series, it works perfectly and the bulb consumes $500\,W.$ The value of $R$ is .................. $\Omega$View Solution
- 7In a neon discharge tube $2.9 \times {10^{18}}\,N{e^ + }$ ions move to the right each second while $1.2 \times {10^{18}}$ electrons move to the left per second. Electron charge is $1.6 \times {10^{ - 19}}\,C$. The current in the discharge tubeView Solution
- 8If a $30\, V$, $90\, W$ bulb is to be worked on a $120\, V$ line, a resistance of how many ohms should be connected in series with the bulb ............... $ohm$View Solution
- 9Potential difference between the points $P$ and $Q$ in the electric circuit shown is ................. $V$View Solution
- 10View SolutionWhich of the following is not a correct statement