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