Question

10 kj/s of heat is produced when a DC flows through a 100 ohm resistor. Which of the following ac produces nearly same heat per sec through the same resistor
(A) I= 15 sin wt (B) I=45 sin wt (C) I= 30 sin wt (D) I= 10 sin wt

Answer 1

Answer:

15 sin wt

Explanation:

Since, from the question that 10 kJ/s or 10 kW  is the power which is dissipated through the 100 ohm resistor. So, we will get the current as

P=i × R = i × 100 = 10000 which on solving we will get  i = 10 A .

 So, the RMS value will give us the value same or near about same as of the current flown in the 100 ohm resistor.

 

So, the RMS value of 15 sinωt  will be  15/√2 = 10.6 A .

Of 45 sinωt  A:-  45/√2 = 31.8 A .

For 30 sinωt  A:-  30/√2 = 21.2 A .

And 10 sinωt  A:-  10/√2 = 7.07 A .

 

So, from the above observation we see that the current in the 15 sinωt A  is same or near to the 10 kW which is in 100 ohm resistor.