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: Heat Produced in a Conductor Formula
The heat \( H \) generated in a conductor by a steady current \( I \) flowing for time \( t \) is calculated using the formula:
\[H = I^2 R t\]Variables are defined as:
- \( I \): Current in amperes (A)
- \( R \): Conductor resistance in ohms (Ω)
- \( t \): Time in seconds (s)

Step 2: Formula Derivation
Heat generation in a conductor by current arises from the work done against resistance. The power dissipated as heat is:
\[P = I^2 R\]Since power is the rate of work (energy/heat per unit time), the total heat \( H \) over time \( t \) is:
\[H = P \times t = I^2 R \times t\]Therefore, the heat produced is \( H = I^2 R t \).

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