MP Board · Class 10 · Science · ElectricityExplain Joule's Law of Heating in detail. Derive the formula for heat produced in a resistor and solve the following: An electric iron of resistance 20 \(\Omega\) takes a current of 5 A. Calculate the heat developed in 30 seconds.

Joule's Law of Heating

\nJoule's law of heating states that the heat produced in a resistor is directly proportional to:

1. The square of the current ((I^2)) flowing through the resistor.
2. The resistance ((R)) of the resistor.
3. The time ((t)) for which the current flows. \nMathematically, it can be expressed as: [H = I^2 R t]

Derivation of the Formula\nWhen an electric charge (Q) moves through a potential difference (V), the work done (W) is given by:

[W = V \times Q]\nSince (Q = I \times t), we get: [W = V \times I \times t]\nAccording to Ohm's law, (V = IR). Substituting (V) in the work done equation, we get: [W = (IR) \times I \times t = I^2 R t]\nAssuming all electrical work done is converted into heat energy (H), we have: [H = I^2 R t]

Numerical Problem Solution

Given Data:

• Resistance ((R)) = 20 (\Omega)
• Current ((I)) = 5 A
• Time ((t)) = 30 seconds

Formula: [H = I^2 R t]

Step-by-Step Calculation:

1. Square the current: (I^2 = 5^2 = 25 \text{ A}^2)
2. Multiply by resistance: (I^2 \times R = 25 \times 20 = 500 \text{ V}\cdot\text{A} = 500 \text{ W})
3. Multiply by time: (H = 500 \times 30 = 15000 \text{ Joules (J)})

Answer:\nThe heat developed in the electric iron is 15,000 J or 15 kJ.