Answered: Nichrome wire of cross- sectional…

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN:9781133939146

Author:Katz, Debora M.

Publisher:Katz, Debora M.

Chapter28: Current And Resistance

Section: Chapter Questions

Problem 65PQ

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Question

Nichrome wire of cross- sectional radius 0.545 mm is to be used in winding a heating coil. If the coil must carry a current of 6.30 A when a voltage of 120 V is applied across its ends, find (a) the required resistance of the coil. (b) the length of wire you must use to wind the coil.

Note: For Nichrome, the resistivity, ρ, is 150x10^-8 Ω·m.

Expert Solution

Step 1

Given data

The radius is $r = 0.545 mm$

The current is $I_{o} = 6.30 A$

The voltage is $V_{o} = 120 V$

The resistivity is $ρ = 150 \times 10^{- 8} Ωm$

(a)

The resistance is,

$\begin{array}{rcl} R_{o} & = & \frac{V_{o}}{I_{o}} \\ = & \frac{120 V}{6.30 A} \\ = & 19.04 Ω \end{array}$

Thus, the resistance is $\begin{array}{rcl} 19 \end{array} \begin{array}{rcl} . \end{array} \begin{array}{rcl} 04 \end{array} \begin{array}{rcl} \end{array} \begin{array}{rcl} Ω \end{array}$

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