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  • The four arms of a Wheatstone bridge have resistances as shsown in the figure. A galvanometer of resistance is connected across BD. Calculate the current through the galvanometer when a

The four arms of a Wheatstone bridge have resistances as shsown in the figure. A galvanometer of 15\; \Omega resistance is connected across BD. Calculate the current through the galvanometer when a potentail difference of 10\; V is maintained across AC.
 
Option: 1 2.44\; mA
Option: 2 4.87\; \mu A
Option: 3 2.44\; \mu A  
Option: 4 4.87\; m A

Answers (1)

best_answer

 

A is directly connected to positive terminal of battery so, VA = 10 V and VC = 0 V

Let VB = x V and VD = y V

So,

By Nodal analysis at B and D -

\begin{aligned} &\frac{x-10}{100}+\frac{x-y}{15}+\frac{x-0}{10}=0\\ &53 x-20 y=30 \ldots \ldots(1)\\ &\frac{y-10}{60}+\frac{y-x}{15}+\frac{y-0}{5}=0\\ &17 y-4 x=10 \ldots \ldots (2)\end{aligned}

on  solving  (1)  &  (2)

\begin{array}{l} x=0.865 \\ y=0.792 \\ \Delta V=0.073 \mathrm{R}=15 \Omega \\ \mathrm{i}=4.87 \mathrm{~mA} \end{array}

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Deependra Verma

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