A steady current of magnitude I and an AC current of peak value I is allowed to pass through the identical resistors for the same time. The ratio of heat production in the two resistors will be:

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2:1

1: 2

1: 1

None of these

answer is A.

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Detailed Solution

Concept- In this question we first find the heat produce by a DC current passing through resistor

that is

then we find the heat produce by an AC current passing through an identical resistor

that is

here we take the RMS value of current that is

. After that we find the ratio as 2: 1
First, we consider the heat produced when DC current

is flowing through a resistor

in the circuit that is

Similarly, the heat produces when an AC current with peak value

is passing through a resistor

in the circuit. Here the RMS value of current

is responsible for the heat that is

We now have the heat produced by the DC and AC current. In the question, we are asked to find the ratio of the heat produced by the DC circuit and the heat produced by the AC circuit.
For this we divide equation number (1) with equation number (2) and we will get
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