question_answer

In the circuit shown below, the cells A and B have negligible resistance. For\[{{\operatorname{V}}_{A}}=12V\], \[{{\operatorname{R}}_{1}} = 500\Omega  and r = 100\Omega ,\]the galvanometer (G) shows no deflection. The value of V,, is:            

A) 4V                               

B) 2V  

C) 12V                 

D) 6V

Correct Answer: B

Solution :

galvanometer show no deflection that implies no current passes through it potential different drop across \[{{\operatorname{R}}_{1}}=\] In series voltage divides while current is same in parallel current divide while voltage is same \[={{V}_{A}}\frac{{{R}_{1}}}{{{R}_{1}}+R}\] \[=12\times \frac{500}{\left( 500+100 \right)}=10V\] Potential different across R=12-10=2V \[{{\operatorname{V}}_{B}}\]=2V [R is parallel to upper circuit]