Question

Derive the formula P = VI of electric power

Answer 1

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Answer 2

Explanation:

According to the joule’s law of heating which states that the heat produced is proportional  

1. Square of the current
2. Resistance of the circuit R
3. The time t during which the current flows through the circuit.

Mathematically,

$H=I^{2}Rt$

Again,

Power is defined as the heat per second.

Therefore,

$Power = \frac{H}{t}$

$Power=\frac{I^{2}Rt}{t}$

$Power = I^{2}R$

According to Ohm's Law:

V = IR

Or

$R=\frac{V}{I}$

Put this value in power equation, we get

$Power = I^{2}\frac{V}{I}$

$Power = VI$

Therefore,  

P = VI

Hence, Proved.