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. $\frac{50}{3} \text{ Ω}$
• D. $\frac{70}{3} \text{ Ω}$

Answer 1

Answer: (A)

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