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)

$\therefore I_G=\frac{10}{100+G}$
$300I_3=\frac{10}{100+G}G$
$I_3=\frac{G}{30}\left[\frac{1}{100+G}\right]$
$\therefore I_3+I_G=\frac{1}{(100+G)}\left[10+\frac{G}{30}\right]=\frac{(300+G)}{(100+G)\times 30}$
According to the problem,
$10=\left(\frac{200}{3}+\frac{300G}{300+G}\right)\left[\frac{(300+G)}{(100+G)30}\right][\because V=RI]$
$10=\frac{60000+1100G}{3}\times \frac{1}{100+G}\times \frac{1}{30}$
$\Rightarrow 900(100+G)=60000+1100G$
$\Rightarrow 30000=200G$
$\therefore G=150\Omega$
$I_G=\frac{10}{100+150}=\frac{10}{250}=40mA$
As $\frac{200}{100}=\frac{300}{150}$
So, $I_{200}=I_{300}$