A series combination of resistor 'R' and capacitor 'C' is connected to an a.c. source of angular frequency ' ω '. Keeping the voltage same, if the frequency is changed to (ω)/(3) the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is (a) √(0.6) (b) √(6) (c) √(3) (d) √(2)

Answer: (a). At (ω)/(3), XC → 3XC; current halves so R² + 9XC² = 4(R² + XC²). 5XC² = 3R² ⇒ XC/R = √(0.6) So the answer is (a) √(0.6).

A series combination of resistor 'R' and capacitor 'C' is connected… | MHT CET 2021 (21 Sep, Shift 1)

Q42MHT CET 2021 · 21 SEP · SHIFT 1Medium

RL and RC Series Circuits

A series combination of resistor 'R' and capacitor 'C' is connected to an a.c. source of angular frequency ' $\omega$ '. Keeping the voltage same, if the frequency is changed to $\frac{\omega}{3}$ the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is

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Answer: (a)

At $\frac{\omega}{3}$ , $X_C \to 3X_C$ ; current halves so $R^2 + 9X_C^2 = 4(R^2 + X_C^2)$ .
$5X_C^2 = 3R^2 \Rightarrow \frac{X_C}{R} = \sqrt{0.6}$
So the answer is (a) $\sqrt{0.6}$ .

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