A nichrome wire ( = 1.0 × 10^ -6 m ) is used to build a heater coil intended to operate at 500 W when connected to a 250 V supply. Determine the resistance of the coil.

Correct answer: A. 125 Given power of the heater coil, P = 500 W Operating voltage, V = 250 V The resistance of the coil is related to power and voltage by the formula: P = (V^2)/(R) Rearranging for resistance R : R = (V^2)/(P) Substituting the given values: R = (250 × 250)/(500) R = (250)/(2) = 125 The resistivity of nichrome is extra information and is not required to find the resistance.

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 nichrome wire ( = 1.0 × 10^ -6 m ) is used to build a heater coil...

A nichrome wire (

\rho = 1.0 \times 10^{-6} \Omega \text{m}

) is used to build a heater coil intended to operate at

500 \text{ W}

when connected to a

250 \text{ V}

supply. Determine the resistance of the coil.

Options

A $125 \Omega$
B $62.5 \Omega$
C $250 \Omega$
D $500 \Omega$

Correct answer

A. $125 \Omega$

Step-by-step solution

Given power of the heater coil,

P = 500 \text{ W}

Operating voltage,

V = 250 \text{ V}

The resistance of the coil is related to power and voltage by the formula:

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

Rearranging for resistance

R

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

Substituting the given values:

R = \dfrac{250 \times 250}{500}

R = \dfrac{250}{2} = 125 \Omega

The resistivity of nichrome is extra information and is not required to find the resistance.

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