A nichrome wire ( = 1.0 × 10^ -6 m ) with a cross-sectional area of 0.5 mm^2 is used to wrap a heater coil that operates at 500 W when connected to a 250 V supply. If each turn of the coil has a radius of 4.0 mm

Correct answer: D. 2500 Power of the heater coil is given by P = (V^2)/(R) Resistance of the coil, R = (V^2)/(P) = ((250)^2)/(500) = 125 Using the formula for resistance, R = (L)/(A) Total length of the wire, L = (RA)/( ) = 125 × 0.5 × 10^ -6 1.0 × 10^ -6 = 62.5 m Length of one turn of the coil is the circumference, C = 2π r = 2 × π × 4.0 × 10^ -3 = 8π × 10^ -3 m Number of turns, N = (L)/(C) = 62.5 8π × 10^ -3 N = (62500)/(8π) (7812.5)/(3.1416) 2487 Therefore, the number of turns is approximately 2500 .

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 ) with a cross-sectional area of...

A nichrome wire (

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

) with a cross-sectional area of

0.5 \text{ mm}^2

is used to wrap a heater coil that operates at

500 \text{ W}

when connected to a

250 \text{ V}

supply. If each turn of the coil has a radius of

4.0 \text{ mm}

, approximately how many turns will the coil contain?

Options

A $7800$
B $5000$
C $1250$
D $2500$

Correct answer

D. $2500$

Step-by-step solution

Power of the heater coil is given by

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

Resistance of the coil,

R = \dfrac{V^2}{P} = \dfrac{(250)^2}{500} = 125 \Omega

Using the formula for resistance,

R = \rho \dfrac{L}{A}

Total length of the wire,

L = \dfrac{RA}{\rho} = \dfrac{125 \times 0.5 \times 10^{-6}}{1.0 \times 10^{-6}} = 62.5 \text{ m}

Length of one turn of the coil is the circumference,

C = 2\pi r = 2 \times \pi \times 4.0 \times 10^{-3} = 8\pi \times 10^{-3} \text{ m}

Number of turns,

N = \dfrac{L}{C} = \dfrac{62.5}{8\pi \times 10^{-3}}

N = \dfrac{62500}{8\pi} \approx \dfrac{7812.5}{3.1416} \approx 2487

Therefore, the number of turns is approximately

2500

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