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Derive An Expression For Electric Energy
Assuming electrical energy is consumed in a device, let us derive an expression for it in terms of V, I and t, where V is the potential difference applied to it, I is the current drawn by it and t is the time for which the current flows.
We know that work is done in an electrical device = W = QV where Q is an electric charge in coulombs.
Therefore, P = $\frac{W}{t}$ where P is power in watts is the rate of doing work
Now, P = $\frac{QV}{t} = I $ \times $ V where I is current in amps which is the rate of charge flow
⇒ We know V = IR from Ohms law
⇒ P = $\frac{Q}{t}IR$ = I $ \times $ V = I $ \times $ IR = $I^2R$
⇒ Energy = P $ \times $ t
⇒ Energy = $I^2R$ $ \times $ t
⇒ Energy = $\frac{V}{R^2} \times $ R $ \times $ t
⇒ Energy = $\frac{V^2}{R} \times $ t
⇒ Energy = $\frac{V^2}{R} \times $ t Answer
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