If the current I through a resistor is increased by 100% (assume that temperature remains unchanged), the increase in power dissipated will be?

If the current I through a resistor is increased by 100% ,assume

If the current

I

through a resistor is increased by

100 %

, the increase in power dissipated will be

300 %

.
It is given that the current flowing the resistor is

I

is increased by

100 %

.
Since, the relation between power and current is given by

P \propto I²

So,

\frac{P_{2}}{P_{1}} = (\frac{I_{1} ²}{I_{2} ²}) = \frac{(2 I) ²}{I²} = 4

\Rightarrow P_{2} = 4 P_{1}

The percentage increase in power is equal to,

\Rightarrow \frac{P_{2} - P_{1}}{P_{1}} \times 100

\Rightarrow \frac{4 P - P}{P} \times 100 = 300 %

Hence, the increase in power is

300 %

if the current is increased by

100 %

.
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