(a) Write the mathematical expression for Joule's law of heating.

(b) Compute the heat generated while transferring $96000\text{ coulomb}$ of charge in two hours through a potential difference of $40\text{ V}$ .

Electricity

Heating Effect of Electric Current

Official Answer

(a) The mathematical expression for Joule's law of heating is:

$H = I^2 R t$

where $H$ is the heat produced, $I$ is the current flowing through the conductor, $R$ is the resistance of the conductor, and $t$ is the time for which the current flows.

(b) The heat generated is $3.84 \times 10^6 \text{ J}$ (or $3.84 \text{ MJ}$ ).

H = I^2 R tH = VQ3.84 \times 10^6 J3,840,000 J

Marking Scheme

11 mark for writing the correct mathematical expression of Joule's law of heating: $H = I^2 R t$ with terms defined.
21 mark for stating the formula $H = V \times Q$ or calculating the current $I = Q/t$ .
31 mark for substituting the values correctly and obtaining the final answer $3.84 \times 10^6 \text{ J}$ with correct units.

Hint

For part (a), write the formula relating heat ( $H$ ), current ( $I$ ), resistance ( $R$ ), and time ( $t$ ). For part (b), use the direct relation between heat energy, potential difference, and charge: $H = V \times Q$ .

Quick Oral Answer

Joule's law of heating is mathematically expressed as $H = I^2 R t$ . It states that the heat produced in a resistor is directly proportional to the square of the current, the resistance, and the time for which the current flows.

Analysis & Explanation

Joule's law of heating states that the heat generated in a resistor is directly proportional to the square of the current for a given resistance, directly proportional to the resistance for a given current, and directly proportional to the time for which the current flows.

In part (b), we are given the potential difference ( $V$ ) and the total charge ( $Q$ ) transferred. The work done in moving a charge $Q$ through a potential difference $V$ is $W = VQ$ . In a purely resistive circuit, this work is entirely converted into thermal energy (heat). Therefore, the heat generated is simply the product of the potential difference and the charge. The time duration of 2 hours is redundant for the direct calculation ( $H = VQ$ ), but if a student chooses to calculate current first ( $I = Q/t$ ) and then use $H = VIt$ , the time term cancels out, yielding the same correct result.

Common Mistakes

1Unnecessarily multiplying by time in the $H = VQ$ formula, leading to an incorrect value.
2Forgetting to convert hours to seconds if calculating current $I = Q/t$ .
3Omitting the unit (Joules or J) in the final answer.

Interesting Facts

Joule's heating is also known as ohmic heating or resistive heating. It is the principle behind household appliances like electric irons, heaters, and toasters.

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Frequently Asked Questions

How many marks does this question carry in CBSE Class 10 Science 2020?

This question carries 3 marks in the CBSE Class 10 Science 2020 examination.

Which chapter does this question come from in Science?

This question is from the chapter "Electricity" in the CBSE Class 10 Science syllabus.

What topic does this question cover in Science?

This question covers the topic "Heating Effect of Electric Current" from CBSE Class 10 Science.

What type of question is this in the CBSE Class 10 Science 2020 paper?

This is a Short Answer question from Section B in the CBSE Class 10 Science 2020 paper.