First slide

Thermal effect of current

Question

Two electric bulbs rated 25 W, 220 V and 100 W,220 V and connected in series across a 220 V voltage source. The 25 W and 100 W bulbs now draw $P_{1} {and P}_{2}$ powers respectively
(i) $P_{1} = 16 W$ (ii) $P_{1} = 4 W$ (iii) $P_{2} = 16 W$ (iv) $P_{2} = 4 W$

Moderate

A

(i),(iv)
B

(ii),(iii)
C

(i),(iii)
D

(ii),(iv)

Solution

$\Rightarrow R_{1} = \frac{{(220)}^{2}}{25} = 4 R \Rightarrow R_{2} = \frac{{(220)}^{2}}{100} = R \Rightarrow V_{1} = \frac{4 R}{4 R + R} \times 220 = \frac{4}{5} \times 220 V \Rightarrow V_{2} = 220 - V_{1} = \frac{1}{5} \times 220 V \Rightarrow P_{1} = \frac{V_{1}^{2}}{R_{1}} = \frac{{(4 / 5)}^{2} {(220)}^{2}}{{(220)}^{2} / 25} = 16 W \Rightarrow P_{2} = \frac{V_{2}^{2}}{R_{2}} = \frac{{(1 / 5)}^{2} {(220)}^{2}}{{(220)}^{2} / 100} = 4 W$

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