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 , approximately how many turns will the coil contain?

Step-by-step solution

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 = 2 r = 2 4.0 10⁻³ = 8 10⁻³ m Number of turns, N = L C = 62.5 8 10⁻³ N = 62500 8 7812.5 3.1416 2487 Therefore, the number of turns is approximately 2500 .