With the gradual increase in frequency of an a. c. source, the impedance of an LCR series circuit (a) first decreases, becomes minimum and then increases. (b) increases. (c) decreases. (d) remains constant.

Answer: (a). Z = √(R² + (ω L - (1)/(ω C))²). As ω rises, XC - XL first shrinks to zero at ω₀ = (1)/(√(LC)), where Z = R is minimum. Beyond ω₀, XL - XC grows, so Z rises again. So the answer is (a) first decreases, becomes minimum and then increases.

With the gradual increase in frequency of an a. c. source, the… | MHT CET 2023 (11 May, Shift 1)

Q62MHT CET 2023 · 11 MAY · SHIFT 1Easy

Resonance, Bandwidth & Q Factor

With the gradual increase in frequency of an a. c. source, the impedance of an LCR series circuit

Show answer and solution

Answer: (a)

$Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ .
As $\omega$ rises, $X_C - X_L$ first shrinks to zero at $\omega_0 = \frac{1}{\sqrt{LC}}$ , where $Z = R$ is minimum.
Beyond $\omega_0$ , $X_L - X_C$ grows, so $Z$ rises again.
So the answer is (a) first decreases, becomes minimum and then increases.

Report a mistake

Resonance, Bandwidth & Q Factor question from MHT CET 2023 (11 May, Shift 1)

More questions on Resonance, Bandwidth & Q Factor