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Concepts Of Physics MCQ Edition [Volume 2]

Exam: Concepts Of Physics MCQ Edition [Volume 2]
Subject: Physics
Chapter: Thermal and Chemical Effects of Electric Current

Concepts Of Physics MCQ Edition [Volume 2] · Physics · Thermal and Chemical Effects of Electric Current

A heater coil has a specification of 250 V , 500 W . Determine the...

A heater coil has a specification of

250 \text{ V}

,

500 \text{ W}

. Determine the resistance of the coil. Additionally, what will be the resistance of a

1000 \text{ W}

coil designed to operate at the same voltage?

Options

A $250 \Omega$ , $125 \Omega$
B $62.5 \Omega$ , $125 \Omega$
C $125 \Omega$ , $62.5 \Omega$
D $125 \Omega$ , $250 \Omega$

Correct answer

C. $125 \Omega$ , $62.5 \Omega$

Step-by-step solution

The power of a heater coil is given by the relation

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

.

Rearranging for resistance,

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

.

For the first coil with

V = 250 \text{ V}

and

P = 500 \text{ W}

:

R_1 = \dfrac{250^2}{500} = \dfrac{250 \times 250}{500} = \dfrac{250}{2} = 125 \Omega

For the second coil with

V = 250 \text{ V}

and

P = 1000 \text{ W}

:

R_2 = \dfrac{250^2}{1000} = \dfrac{250 \times 250}{1000} = \dfrac{62500}{1000} = 62.5 \Omega

The resistances are

125 \Omega

and

62.5 \Omega

respectively.

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