Page 281 - Basic Electrical Engineering

Let I be the equivalent effective value of the ac flowing through a
resistance element R for a time t, then the amount of heat produced, H is
expressed as

2
2
2
H ∝ I Rt = K I Rt = K I Rt Calories (3.3)
Now, let the alternating current i, be passed through the same resistance R
for the same time t, as shown in Fig. 3.5. Current i has been shown divided
into n intervals and the magnitudes are i , i , i , etc. Heat produced in t
1
2
3
seconds by the ac is equal to the sum of heat produced in n intervals of time
during the time t. This can be expressed as