Question

Derive an expression for the heat produced in a conductor of resistance R when a current I flows through it for time t.

Answer 1

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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

Answer:

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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.