Question

Current I flowing through a resistor results in 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 percent? Justify your answer with the help of mathematical calculations.

Answer 1

Answer:

The power dissipated in the resistor will increase by 125%

Explanation:

if I is the current, R is the resistance, t is the time then power dissipated

$\boxed{P=I^2Rt}$

If the current is increased by 50%, then

$I'=I+I\times\frac{50}{100} =I+\frac{I}{2} =3I/2$

Therefore power

$P'=(\frac{3}{2}I)^2Rt$

$\implies P'=\frac{9}{4}I^2Rt$

Increase in power

$=P'-P$

$=\frac{9}{4}I^2Rt-I^2Rt$

$=\frac{5}{4}I^2Rt$

% Increase in power

$=\frac{(5/4)I^2Rt}{I^2Rt} \times 100$

$=\frac{5}{4} \times 100$

$=125$%

Therefore, the power will increase by 125%

Answer 2

Answer:

current i flowing through a circuit with power p find the increase in percentage of power if the current is increased by 50% by brainy==== 125%