question_answer

In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be

A) \[200\,\Omega \]          

B) \[100\,\Omega \]

C)  \[500\,\Omega \]          

D) \[1000\,\Omega \]

Correct Answer: B

Solution :

 The galvanometer shows zero deflection ie, current through XY is zero. As a result potential drop across R is 2 V, circuit  can be redrawn as \[I=\frac{12}{500+R}\] Voltage across \[R,V=IR\] \[\Rightarrow \] \[2=\frac{12}{500+R}\times R\] \[\Rightarrow \] \[1000+2R=12R\Rightarrow R=100\,\Omega \]