Question

An electric bulb, when connected across a power supply of 220 V, consumes a power of 60 W. If the supply drops to 180 V, what will be the power consumed? If the supply is suddenly increased to 240 V, what will be the power consumed?

Answer 1

The resistance of a bulb that consumes power P and is operated at voltage V is given by
$R=\frac{V^2}{P}=\frac{220\times 220}{60}=806.67\mathrm{\Omega }$

(a) Now the supply drops to V' = 180 V.
So, the power consumed,
$P\text{'}=\frac{V{\mathit{\text{'}}}^2}{R}=\frac{{\left(180\right)}^2}{806.67}=40\mathrm{W}$

(b) Now the supply increases to V" = 240 V. Therefore,
$P"=\frac{{V^{\mathit{\text{'}}\mathit{\text{'}}}}^2}{R}=71\mathrm{W}$