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 \[2V\], circuit can be redrawn as                                     \[I=\frac{12}{500+R}\] Voltage across\[R\],\[V=IR\] \[\Rightarrow \]               \[2=\frac{12}{500+R}\times R\] \[\Rightarrow \]               \[1000+2R=12R\Rightarrow R=100\Omega \]