Question

In an experiment to determine the resistance of a galvanometer by half deflection method, the circuit shown is used. In one set of readings, if $R=10\Omega$ and $S=4\Omega$ , then the resistance of the galvanometer is

• A. $\frac{20}{3}\Omega$
• B. $\frac{40}{3}\Omega$
• C. $\frac{50}{3}\Omega$
• D. $\frac{70}{3}\Omega$

Answer 1

Answer: (A)

In 1st case,
$I_1=\frac{E}{R+G}$
In 2nd case,
$I_2=\frac{E}{R+\frac{SG}{S+G}}$
for half deflection,
$I_{2G}=\frac{1}{2}{I}_1$
$\frac{1}{2}\frac{E}{R+G}=\frac{E}{R+\frac{SG}{S+G}}\frac{S}{S+G}$
$\Rightarrow G=\frac{RS}{R-S}$
$G=\frac{10\times 4}{10-4}=\frac{20}{3}\Omega$