The electric furnace, the resistance of which is 22 ohms, is powered by an alternator.

The electric furnace, the resistance of which is 22 ohms, is powered by an alternator. Determine the amount of heat (in kJ) generated by the oven in one minute if the amplitude of the current is 10 A.

Given:

R = 22 Ohm – resistance of the electric furnace;

I = 10 Amperes – current in the electric furnace;

t = 1 minute = 60 seconds – time span.

It is required to determine Q (Joule) – the amount of heat that will be released by the electric furnace over a period of time t.

Since, according to the condition of the problem, the furnace is connected to an alternator, the effective value of the current will be equal to:

Id = I / 2 ^ 0.5.

Then, the amount of released heat will be equal (according to the Joule-Lenz law):

Q = Id ^ 2 * R * t = (I / 2 ^ 0.5) ^ 2 * R * t = I ^ 2 * R * t / 2 = 10 ^ 2 * 22 * ​​60/2 = 66000 Joules = 66 kJ.

Answer: in 1 minute, an electric furnace will generate heat equal to 66 kJ.