A heater coil is to be constructed with a nichrome wire `(rho = 1.0 xx 10^(-6) Omegam)` which can operate at `500 W` when connected to a `250 V` supply. (a) What would be the resistance of the coil? (b) If the cross-sectional area of the wire is `0.5 mm^2`, what length of the wire will be needed? (c) If the radius of each turn is `4.0 mm`, how many turns will be there in the coil?

Answer

A, B, C

Explanation

`p = 1xx16^(-6) Omega- m, P = 500 W, V = 250V`
` (a) R=(V^2)/(P) = ((250))^2/(500) = 125 Omega`
` (b) `
`A = 0.5 mm^2`
` `
`= 0.5xx10^(-6)`
` `
`= 5xx10^(-7) m^2`
` R = p(l)/(A)`
`l= (AR0/(p) = (125 xx5xx10^(-7)/(1.0xx10^(-6)`
`= 62.5 m`
` (c ) `
`62.5 = rxxn`
`rArr 62.5 = 2xx3.14xx4xx10^(-3)xxn`
` `
`rArr n = 62.5 xx (10^(-3))/(2xx3.14xx4) rArr n= 62.5xx(10^(-3))/(25.12) = 2500 turns`