An electric heater of resistance 44 Ω draws 5 A from the service mains for 2 hours. Calculate the rate at which heat is developed in the heater.
The rate at which heat is developed in the heater is 1100 W (or 1100 J/s).
Explanation
The question asks for the rate at which heat is developed, which is the power of the heater. From Joule's law of heating given in Eq. (11.21), H = I²Rt. The rate of heat development (power) is obtained by dividing heat by time: P = H/t = I²R. The time duration (2 hours) is not required for calculating the rate, as power is independent of time duration.
Solution Steps
Step 1: Identify the given values: Resistance R = 44 Ω, Current I = 5 A, Time t = 2 hours.
Step 2: Understand that the rate at which heat is developed is the power of the heater.
Step 3: From Joule's law of heating, the power is given by P = I²R.
Step 4: Substitute the values: P = (5 A)² × 44 Ω = 25 A² × 44 Ω = 1100 W.