Question

29. Find the ratio of the resistances of a 40 W bulb and a
100 W bulb designed to work at 220 V supply line.
Ans. 5:2.​

Answer 1

Explanation:-

In this question, we are asked to find ratio of resistance of 2 bulbs having powers 40W and 100W each is designed to work at 220V supply. We can find out the ratio of both by applying formula for resistance.

So let's do it!!

Given:-

• Power of bulb 1=40W

• Power of bulb 2=100W

• Voltage supply for both=220V

Formula used:-

• R= V²/P

Solution:-

$\sf :\implies Required\:ratio=\cfrac{R_1(Bulb\; 1)}{R_2(Bulb\;2)}$

Applying formula for resistance:

$\sf :\implies Required\:ratio=\cfrac{\bigg(\cfrac{V^2}{P_1}\bigg)}{\bigg(\cfrac{V^2}{P_2}\bigg)}$

$\sf :\implies Required\:ratio=\cfrac{V^2\times P_2}{P_1\times V^2}}$

Here V² will be cancelled from both numerator and denominator:

$\sf :\implies Required\:ratio=\cfrac{P_2}{P_1}$

By putting given values we get:

$\sf :\implies Required\:ratio=\cfrac{100}{40}$

By solving it we get:

$\sf :\implies Required\:ratio=\cfrac{5}{2}$

$\sf :\implies Required\:ratio=5:2$

So the required ratio is 5:2.

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