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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?
A33 Ω
B11 Ω
C300 Ω
D9 Ω
Answer & Solution
Correct answer: B. 11 Ω
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_
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