Question 17.3: THE RESISTANCE OF NICHROME WIRE GOAL Combine the concept of ...
THE RESISTANCE OF NICHROME WIRE
GOAL Combine the concept of resistivity with Ohm’s law.
PROBLEM (a) Calculate the resistance per unit length of a 22-gauge Nichrome wire of radius 0.321 \mathrm{~mm}. (b) If a potential difference of 10.0 \mathrm{~V} is maintained across a 1.00-\mathrm{m} length of the Nichrome wire, what is the current in the wire? (c) The wire is melted down and recast with twice its original length. Find the new resistance R_{N} as a multiple of the old resistance R_{O}.
STRATEGY Part (a) requires substitution into Equation 17.5,
R = \rho \frac{\ell}{A} [17.5]
after calculating the cross-sectional area, whereas part (b) is a matter of substitution into Ohm’s law. Part (c) requires some algebra. The idea is to take the expression for the new resistance and substitute expressions for \ell_{N} and A_{N}, the new length and cross-sectional area, in terms of the old length and cross section. For the area substitution, remember that the volumes of the old and new wires are the same.
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