Question

The heat developed in an electric wire varies jointly as the wire's resistance, the time the current flows, and the square of the current. In two minutes a current of 5 amps develops 1,200 heat units in a wire of 8 ohms resistance. What resistance does a similar wire have, which develops 6,000 heat units with a current of 10 amps in 5 minutes?

Answer 1

Suppose that, the current c amperes passing through a wire having resistance r ohms for t minutes develops h units of heat.
Then by what is given, h α rtc^2.
Therefore, h=krtc2………..[1], where, k is the constant of variation.
Given that, t=2, c=5, r=8, h=1200.
Substituting in [1], we get, k=h/(rtc2)=1200/(8*2*25)=3.
Hence, [1] becomes, h=3rtc2………………[1’]
Now, we require, r for h=6000, c=10 and t=5.
Substituting in [1’], we have, 6000=3*r*5*100.
Clearly, r=6000/(3*5*100)=4 ohms.