Question

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

Answer 1

Step 1: Formula for heat produced in a conductor
The amount of heat \( H \) produced in a conductor when a steady current \( I \) flows through it for a time \( t \) is given by the formula:
\[ H = I^2 R t \] where:
- \( I \) is the current in amperes (A),
- \( R \) is the resistance of the conductor in ohms (Ω),
- \( t \) is the time in seconds (s).

Step 2: Derivation of the formula
The heat produced in a conductor due to the current can also be obtained from the work done to move charges against resistance. The power dissipated as heat in the conductor is:
\[ P = I^2 R \] Power is the rate of work, which means the amount of energy (or heat) dissipated per unit time. So, the energy (heat) produced over a time \( t \) is the product of power and time:
\[ H = P \times t = I^2 R \times t \] Thus, the amount of heat produced in the conductor is \( H = I^2 R t \).

Final Expression:
The expression for the heat produced in a conductor is:
\[ H = I^2 R t \]