question_answer

The galvanometer deflection, when key \[{{K}_{1}}\]is closed but \[{{K}_{2}}\] is open, equals \[{{\theta }_{0}},\] (see figure). On closing \[{{K}_{2}}\]also and adjusting \[{{R}_{2}}\] to \[5\Omega ,\]the deflection in galvanometer becomes\[\frac{{{\theta }_{0}}}{5}.\] The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]                      [JEE Main 12-Jan-2019 Morning]

A) \[25\Omega \]

B) \[22\Omega \]

C) \[5\Omega \]

D) \[12\Omega \]

Correct Answer: B

Solution :

[b] Initially, let be the current through G.

then

After the key is closed, the circuit is shown as Apply KVL on loop 1,

Also,

For a galvanometer,

So,