First slide

Electrical power

Question

Two bulbs of 500 watt and 200 watt are manufactured to operate on 220 volt line. The ratio of heat produced in 500 W and 200 W, in two cases, when firstly they are joined in parallel and secondly in series, will be

Easy

A

$\frac{5}{2}, \frac{2}{5}$
B

$\frac{5}{2}, \frac{5}{2}$
C

$\frac{2}{5}, \frac{5}{2}$
D

$\frac{2}{5}, \frac{2}{5}$

Solution

Resistance R₁ of 500 W bulb $= \frac{{(220)}^{2}}{500}$
Resistance R₂ of 200 W bulb $= \frac{{(220)}^{2}}{200}$
When joined in parallel, the potential difference across both the bulbs will be same.
Ratio of heat produced $= \frac{V^{2} / R_{1}}{V^{2} / R_{2}} = \frac{R_{2}}{R_{1}} = \frac{5}{2}$
when joined in series, the same current will flow through both the bulbs.
Ratio of heat produced $= \frac{i^{2} R_{1}}{i^{2} R_{2}} = \frac{R_{1}}{R_{2}} = \frac{2}{5}$

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