Heat energy is produced in a resistor of a circuit at the rate of 100 W while a current of 3 A flows through it. What is the value of the resistance?

1. Rate of heat is power, so $P = 100$ W and $I = 3$ A. 2. From Joule's law $P = I^2 R$, so $R = \dfrac{P}{I^2}$. 3. Substitute: $R = \dfrac{100}{3^2} = \dfrac{100}{9}$. 4. $R \approx 11\ \Omega$. 5. The option 33 Ω comes from dividing by I instead of I² ($100/3 \approx 33$), which is the wrong form of the law. _Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 4 "Effects of Electric Current", p.69_