Question

Full scale deflection current for a galvanometer is $1mA$. The value of shunt resistance (approximately) so that galvanometer shows half scale deflection is

• A. $1.5$ m$\Omega$
• B. $3$ m$\Omega$
• C. $10$ m$\Omega$
• D. $15$ m$\Omega$

Answer 1

The correct option is A $1.5$ m$\Omega$

In the given part of circuit,
the full scale deflection current through galvanometer is
$I_{fsd}={10}^{-3}A$
When shunt resistance is introduced in the circuit galvanometer shows half scale deflection current
$I_{hsd}=\frac{1}{2}{10}^{-3}A$

Therefore,
$\frac{1}{2}{10}^{-3}\left(30\right)=S[10-\frac{1}{2}{10}^{-3}]$
$S=\frac{30\times {10}^{-3}}{20-{10}^{-3}}$

Hence,
$S=\frac{30}{20000-1}\cong \frac{30}{20000}\cong 1.5$m$\Omega .$