Calculate the current through a 60 W lamp rated for 250 V. If the line voltage falls to 200 V, how is power consumed by the lamp affected?

Given,

Power (P) = 60 W

Voltage (V) = 250 V

We know that,

Power (P) = VI

Substituting the values in the formula above, we get,

$60 = 250 \times I \\[0.5em] \Rightarrow I = \dfrac{60}{250} \\[0.5em] \Rightarrow I = 0.24 A$

Hence, current through the lamp = 0.24 A

Power consumed when voltage is 200 V = ?

Resistance of lamp (R) = $\dfrac{V^2}{P}$

Substituting the values in the formula, we get,

$R = \dfrac{250^2}{60} \\[0.5em] \Rightarrow R = 1041.6 Ω$

From relation,

P = $\dfrac{V^2}{R}$

Substituting the values in the formula, we get,

$P = \dfrac{200^2}{1041.6} \\[0.5em] \Rightarrow P = 38.4 W$

Hence, power consumed reduces to 38.4 W