A heater coil, designed to operate at 500 W across a 250 V supply, is fabricated from a nichrome wire having a resistivity of 1.0 10⁻⁶ m . If the wire has a cross-sectional area of 0.5 mm ^2 , what is the required length of the wire?

Step-by-step solution

The resistance of the heater coil is given by the formula: R = V^2 P Substituting the given values V = 250 V and P = 500 W : R = (250)^2 500 = 62500 500 = 125 The resistance of a wire is related to its length L , cross-sectional area A , and resistivity by: R = L A Rearranging for length L : L = R A Given = 1.0 10⁻⁶ m and A = 0.5 mm ^2 = 0.5 10⁻⁶ m ^2 , substituting these values gives: L = 125 0.5 10⁻⁶ 1.0 10⁻⁶ L = 125 0.5 = 62.5 m