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A parallel connection to an electrical supply is made up of three incandescent bulbs with respective ratings of $A 40 W, B 60 W, and C 100 W$ . Which of the choices below is true?

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Brightness of all the bulbs will be equal

Brightness of bulb

B

will be more than that of

C

Brightness of bulb

A

will be the highest

Brightness of bulb

A

will be less than that of

B

answer is D.

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Detailed Solution

If in an electric circuit, three incandescent bulbs

A

B

and

C

of rating

40 W

60 W

and

100 W

respectively are connected in parallel to an electric source then brightness of bulb

B

will be more than that of

A

.
It is given that the bulbs of power

P_{A} = 40 W

P_{B} = 60 W

P_{C} = 100 W

are connected in parallel.
It is known that the power drawn

(P)

by a component can be given as

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

Where

V

is the voltage and

R

is the resistance of the component.
It can also be written as

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

Substituting the values of the powers of the bulb

A

B

and

C

, we get their respective resistances as

R_{A} = \frac{V^{2}}{40}

R_{B} = \frac{V^{2}}{60}

R_{C} = \frac{V^{2}}{100}

where

R_{a,} R_{b}, R_{c}

are the resistances of A, B and C respectively.
Therefore, from the above relations, it can be said that

R_{A} > R_{B} > R_{C}

.
Since power is inversely proportional to resistance, the bulb with lower resistance will glow brighter. Hence, the brightness of bulb

B

will be more than that of

A

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A parallel connection to an electrical supply is made up of three incandescent bulbs with respective ratings of A 40 W,B 60 W,and C 100 W. Which of the choices below is true?

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A parallel connection to an electrical supply is made up of three incandescent bulbs with respective ratings of $A 40 W, B 60 W, and C 100 W$ . Which of the choices below is true?