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# two wires aand b of the same material having same length have their cross section areas in ratio 1ratio6 . what would be the ratio of heat produced in these wires when same voltage is applied across each?

Sanju
106 Points
3 years ago
Given that the cross section area of wire a & b are in the ratio 1:6
We have, H = I2RT   & R = ρL/A
where H = heat produced, I = current, R = resistance, T=time, ρ=resistivity of the material, L = length of the wire and A = area of cross section..
Substituting the relation R = ρL/A in the eqn  H = I2RT
H = I2(ρL/A)T
Since A1: A2 = 1:6, the ratio of heat produced in wire a & b is:
H1: H2 = A2:A1 = 6:1

The ratio of heat produced in the wire a & b when same voltage is applied across each wire = 6:1