Question 511: Current Electricity

Question

If only $5 \%$ of the total current is to be passed through galvanometer of resistance G , then the resistance of the shunt will be

Accepted Answer

Let the total current be $I$.
Only $5\%$ of $I$ should pass through the galvanometer.
So, current through galvanometer,
$$ I_g = \frac{5}{100}I = \frac{I}{20} $$
Current through shunt,
$$ I_{sh} = I - I_g = I - \frac{I}{20} = \frac{19I}{20} $$
If $G$ is the resistance of galvanometer and $S$ is the resistance of the shunt, both are in parallel across the same voltage.
By Ohm's Law:
$$ 	ext{Voltage across } G = 	ext{Voltage across } S $$
$$ I_g \cdot G = I_{sh} \cdot S $$
Substitute the values:
$$ \frac{I}{20} \cdot G = \frac{19I}{20} \cdot S $$
Divide both sides by $I$:
$$ \frac{1}{20}G = \frac{19}{20}S $$
Divide both sides by $\frac{19}{20}$:
$$ S = \frac{1}{20}G 	imes \frac{1}{\frac{19}{20}} $$
$$ S = \frac{G}{19} $$
Correct Option:
$ \boxed{\frac{G}{19}} $
So, the right answer is Option C.

Answer

$\frac{\mathrm{G}}{15}$

Answer

$\frac{\mathrm{G}}{17}$

Answer

$\frac{\mathrm{G}}{19}$

Answer

$\frac{\mathrm{G}}{21}$

Current Electricity

If only 5 \% of the total current is to be passed through galvanometer of resistance G , then the resistance of the shunt will be

Choose the correct answer: