When an inductor ' L ' and a resistor ' R ' in series are connected across a 15 V, 50 Hz a.c. supply, a current of 0.3 A flows in the circuit. The current differs in phase from applied voltage by (π/3)c. The value of ' R ' is (sin π/6 = cos π/3 = 1/2, sin π/3 = cos π/6 = √(3)/2) (a) 10 Ω (b) 15 Ω (c) 20 Ω (d) 25 Ω

Answer: (d). Z = V/I = 15/0.3 = 50 Ω R = Zcos φ = 50 × cos π/3 = 25 Ω So the answer is (d) 25 Ω.

When an inductor ' L ' and a resistor ' R ' in series are connected… | MHT CET 2023 (12 May, Shift 2)

Q35MHT CET 2023 · 12 MAY · SHIFT 2Medium

RL and RC Series Circuits

When an inductor ' $L$ ' and a resistor ' $R$ ' in series are connected across a $15\text{ V},\ 50\text{ Hz}$ a.c. supply, a current of $0.3\text{ A}$ flows in the circuit. The current differs in phase from applied voltage by $\left(\frac{\pi}{3}\right)^{c}$ . The value of ' $R$ ' is $\left(\sin\frac{\pi}{6} = \cos\frac{\pi}{3} = \frac{1}{2},\ \sin\frac{\pi}{3} = \cos\frac{\pi}{6} = \frac{\sqrt{3}}{2}\right)$

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Answer: (d)

$Z = \frac{V}{I} = \frac{15}{0.3} = 50\ \Omega$
$R = Z\cos\phi = 50 \times \cos\frac{\pi}{3} = 25\ \Omega$
So the answer is (d) $25\ \Omega$ .

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