1. Two wires A and B of same material and same length have their cross sectional areas in ratio 1:4 .What should be the ratio of heat produced in these wires when same voltage is applied across each other ?

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Solution

Heat produced ,
H=(I^2)Rt=(V^2 /R)t

ie,H inversely proportional to Resistance,R

So,ratio of heat is equal to inverse of ratio of resistance for same voltage and time.

We know resistance,
R=ρL/A

Since length,L is same R is proportional to inverse of area.

So,ratio of resistance will be inverse of ratio of areas.
ie, R1:R2=4:1

So,heat produced is in the inverse ratio of resistance.

ie,H1:H2=1:4

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