Current I flowing through 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%? Justify your answer with the help of mathematical calculations.

Explanation

The power dissipated in the resistor will increase by 125%
`P= I^(2)Rt`
When I is increased by 50% I becomes `(3)/(2)I`.
Hence, `P. =((3)/(2)I)^(2)Rt= (9)/(4)I^(2)Rt`
Increase in power dissipation = `(9)/(4)I^(2)Rt- I^(2)Rt`
`(5)/(4)I^(2)Rt`
`" Percentage increase"= ("increase")/("decrease") xx 100`
`= (5I^(2)Rt)/(4I^(2)Rt) xx 100`
125%