Q. 4

A heater coil is to be constructed with a nichrome wire (ρ = 1.0 × 10–8 Ω m) 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 mm2, 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) Let R be the resistance of the coil.


Given, resistivity, ρ = 1.0 × 10–8 Ω m


The power P consumed by a coil of resistance R when connected across a supply V is given by Joule’s heating effect-






(b) We know resistance R is given by-



where


ρ = resistivity of the material


l = length of the wire


A= area of cross section of the wire


Given, cross-sectional area of the wire is 0.5 mm2





(c) Let n be the number of turns in the given coil.


Given, radius of each turn is 4.0 mm


Then,



Where,


l = length of the coil


r=radius of the coil





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