Question

Derive an expression for the heat produced in time 't' in a wire or resistance 'R',which carrying a conductor 'I'?

Answer 1

Here is your answer-

Consider a resistor of Resistance R. Let the current flowing through the resistor be I and potential difference across its ends be V.
In time t, let Q amount of charge flows through the resistor.

Work done on Moving charge will be,
W =V x Q ---------(1).

According to the definition of electric current,
Q = I x t -----------(2).

Putting equation (2) in (1),
W = V x I x t.
And the work done is dissipated as heat.
Therefore,
Heat produced, H=W=V x I x t => VIt.
H= VIt.
According to Ohm's law V= IR.
Putting this in equation(2), we get,
H= IR x It.
Therefore, Heat= I2(square)Rt.
I square x R x t.

Answer 2

Hui friends

Let's take the values in variables

Let current be I

Potential difference be V

Amount ofWork done be W

Charge be Q

And time be t

We know that work done is equal to the product of potential difference and charge

i.e. W = VQ---------------1

Also Q = It---------------2

Therefore from 1 & 2

We can say that

W= VIt

Also we know that

Work done = Energy = Heat

Thus, we can write that

Heat(H)= VIt

Hence proved

Hope it might help you.

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