Question

The efficiency of a cell when connected to a resistance $R$ is $60$%. What will be its efficiency of the external resistance is increased to six times.

• A. $80$%
• B. $90$%
• C. $55$%
• D. $95$%

Answer 1

The correct option is B $90$%

Given: The efficiency of a cell when connected to a resistance R is $60\%$

To find the efficiency of the external resistance is increased to six times.

Solution:

Formula used:

efficiency of the cell, $\eta =\frac{\text{useful power}}{\text{total power produced}}$

then if,

$r$ = internal resistance of the cell

$R$ = external resistance

$I$ = currentproduced

Then

$\eta =\frac{I^{2}R}{I^{2}r+I^{2}R}⟹\eta =\frac{R}{r+R}⟹0.6=\frac{R}{R+r}⟹0.6R+0.6r=R⟹R=1.5r$

Therefore, when resistance $R$ becomes 6 times its original value then the new efficiency ${\eta }_2$ will be

${\eta }_2=\frac{6R}{(6R+r)}⟹{\eta }_2=\frac{6\left(1.5r\right)}{6\left(1.5r\right)+r}⟹{\eta }_2=\frac{9r}{10r}⟹{\eta }_2=0.9⟹90\%$

will be the efficiency of the external resistance is increased to six times.