Question

A non-zero current passes through the galvanometer $G$ shown in the circuit when the key ‘$K$’ is closed and its value does not change when the key is opened. Then which of the following statement(s) is/are true ?

• A. The galvanometer resistance is infinite.
• B. The current through the galvanometer is 40 mA.
• C. After the key is closed, the current through the $200 \, \Omega$ resistor is same as the current through the $300 \, \Omega$ resistor.
• D. The galvanometer resistance is $150 \,\Omega$ .

Answer 1

Answer: (B), (C), (D)

$\therefore I_{G} =\frac{10}{100+G} $
$300 I_{3} =\frac{10}{100+G} G$
$I_{3} =\frac{G}{30}\left[\frac{1}{100+G}\right]$
$\therefore I_{3}+I_{G}=\frac{1}{(100+G)}\left[10+\frac{G}{30}\right]=\frac{(300+G)}{(100+G) \times 30}$
According to the problem,
$10=\left(\frac{200}{3}+\frac{300 G}{300+G}\right)\left[\frac{(300+G)}{(100+G) 30}\right] [\because V = RI]$
$10=\frac{60000+1100 G}{3} \times \frac{1}{100+G} \times \frac{1}{30}$
$\Rightarrow 900(100+G)=60000+1100 G$
$\Rightarrow 30000=200 \,G$
$\therefore G=150\, \Omega$
$I_{G}=\frac{10}{100+150}=\frac{10}{250}=40 \,mA$
As $ \frac{200}{100}=\frac{300}{150}$
So, $ I_{200}=I_{300}$