Two wire A and B with circular cross-sections having identical lengths and are made of the same material. Yet, wire A has four times the resistance of wire B. How many times greater is the diameter of wire B than wire A?
If wire A has four times the resistance, then it must have the smaller cross-sectional area since resistance and cross-sectional area are inversely proportional. In fact, A must have one-fourth the cross-sectional area of B. Since the cross-sectional area of a circular cross-section is given by the expression:
wire A must have one-half the radius of wire B and therefore one-half the diameter. Put another way, the diameter of wire B is two times greater than the diameter of wire A.
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