Question

what will be the percentage increase in power across each circuit if the current is increased by 2%

Answer 1

Keeping all other parameters constant, if the current in the circuit is increased by 2%, the increase in power will be 4.04%.

Power is proportional to I*I and hence new power will be (1.02*1.02)*Original Power.

Answer 2

The percentage increase in power across each circuit is 4.04%.

Explanation:

Given that,

Current I'=1.02 I

We need to calculate the initial power

Using formula of power

$P=I^2R$...(I)

Increased power,

$P'=I'^2R$...(II)

Divided equation (I) by (II)

$\dfrac{P}{P'}=\dfrac{I^2R}{I'^2R}$

Put the value into the formula

$\dfrac{P}{P'}=\dfrac{I^2R}{(1.02 I)^2R}$

$P=0.961P'$

We need to calculate the percentage increase in power across each circuit

Percentage increase in power

$P\%=\dfrac{P'-P}{P}\times100$

Put the value into the formula

$P\%=\dfrac{P'-0.961 P'}{0.961P'}\times100$

$P\%=\dfrac{0.0388}{0.961}\times 100$

$P\%=4.04\%$

Hence, The percentage increase in power across each circuit is 4.04%.

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Topic : power

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