Question

The current sensitivity of a galvanometer increase by 20%. If its resistance also increases by 25%, the voltage sensitivity will ______.

Options

• decrease by 1%

• increased by 5%

• increased by 10%

• decrease by 4%

Answer 1

The current sensitivity of a galvanometer increase by 20%. If its resistance also increases by 25%, the voltage sensitivity will decrease by 4%.

Explanation:

Given, ${\displaystyle {\text{I'}}_{\text{g}}={\text{I}}_{\text{g}}+\frac{20}{100}{\text{I}}_{\text{g}}}$

${\displaystyle =\frac{120}{100}{\text{I}}_{\text{g}}=1.2 {\text{I}}_{\text{g}}}$

R' = R + ${\displaystyle \frac{25}{100}\text{R}=\frac{125}{100}\text{R}}$

= 1.25 R

${\displaystyle {\text{V'}}_{\text{g}}}$ = ?

${\displaystyle {\text{V'}}_{\text{g}}=\frac{{\text{I'}}_{\text{g}}}{\text{R'}}=\frac{1.2{\text{I}}_{\text{g}}}{1.25 \text{R}}}$

${\displaystyle =\frac{120}{125}{\text{V}}_{\text{g}}=\frac{25}{25}{\text{V}}_{\text{g}}}$

% change = ${\displaystyle \frac{{\text{V'}}_{\text{g}}-{\text{V}}_{\text{g}}}{{\text{V}}_{\text{g}}}\times 100}$

${\displaystyle =\frac{(\frac{24}{25}{\text{V}}_{\text{g}}-{\text{V}}_{\text{g}})}{{\text{V}}_{\text{g}}}\times 100}$

${\displaystyle =\frac{(24-25)}{25}\times 100}$

${\displaystyle =\frac{-1}{25}\times 100}$

= 4%