Question

Current I flowing through a resistor results in a dissipation of power P. By what percentage will the power dissipated in the resistor increase if the current through the resistor is increased by $50\%$. Justify your result with the help of mathematical calculation.

Answer 1

Power $=(current{)}^2\times$ resistance

$=I^2\times R$

If $I$ is increased by 50% then $\frac{150}{100}I$

Power $=(\frac{150}{100}{)}^2{I}^2\times R$

Power $=(\frac{9}{4}{)}^2{I}^2\times R$

Increase in power $=(\frac{5}{4}{)}^2{I}^2\times R$

Therefore, % of increase $=\frac{(\frac{5}{4}{)}^2{I}^{2}R}{I^{2}R}\times 100=125$%