# Two electric bulbs rated at 25 W, 220 V and 100 W, 220 V are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw power

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Two electric bulbs rated at 25 W, 220 V and 100 W, 220 V are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P1 and P2 respectively, then
1. P1 = 16 W, P2 = 4 W
2. P1 = 4 W, P2 = 16 W
3. P1 = 9 W, P2 = 16 W
4. P1 = 16 W, P2 = 9 W

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Correct Answer - Option 1 : P1 = 16 W, P2 = 4 W

Concept:

Resistance of a bulb of power P and with a voltage source V is given by the formula:

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

Calculation:

Resistance of the given two bulbs are given as:

${R_1} = \frac{{{V^2}}}{{{P_1}}} = \frac{{{{(220)}^2}}}{{25}}$

${R_2} = \frac{{{V^2}}}{{{P_2}}} = \frac{{{{(220)}^2}}}{{100}}$

Since, bulbs are connected in series. This means same amount of current flows through them.

The current in circuit is given as:

$i = \frac{V}{{{R_{{\rm{total\;}}}}}} = \frac{{220}}{{\frac{{{{(220)}^2}}}{{25}} + \frac{{{{(220)}^2}}}{{100}}}} = \frac{1}{{11}}{\rm{\;A}}$

The power drawn by bulbs are given as:

${{\rm{P}}_1} = {{\rm{i}}^2}{{\rm{R}}_1} = {\left( {\frac{1}{{11}}} \right)^2} \times \frac{{220 \times 220}}{{25}} = 16{\rm{\;W}}$

${{\rm{P}}_2} = {{\rm{i}}^2}{{\rm{R}}_2} = {\left( {\frac{1}{{11}}} \right)^2} \times \frac{{220 \times 220}}{{100}} = 4{\rm{\;W}}$