Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| (Circuits in different combinations) | (Variation of impedance with increase in frequency) | ||
| (A) | AC circuit has a resistor only. | (I) | It increases with increase in frequency. |
| (B) | AC circuit has an inductor only. | (II) | It first decreases and then increases. |
| (C) | AC circuit has a capacitor only. | (III) | It decreases with increase in frequency. |
| (D) | L-C-R series circuit | (IV) | It does not change with frequency. |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) - (IV), (B) - (I), (C) - (III), (D) - (II)
The impedance of each circuit follows from how its reactance depends on the angular frequency ω.
(A) AC circuit has a resistor only. — this matches (IV) It does not change with frequency. Resistance R is independent of frequency.
(B) AC circuit has an inductor only. — this matches (I) It increases with increase in frequency. The inductive reactance is proportional to the frequency.
\( X_{L} = \omega L \)
(C) AC circuit has a capacitor only. — this matches (III) It decreases with increase in frequency. The capacitive reactance is inversely proportional to the frequency.
\( \displaystyle X_{C} = \frac{1}{\omega C} \)
(D) L-C-R series circuit — this matches (II) It first decreases and then increases. Z falls to its minimum value R at resonance, where \( X_{L} = X_{C} \), and rises again beyond it.
\( \displaystyle Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}} \)
NCERT (2026-27):
AC Voltage Applied to an Inductor – “… The inductive reactance is directly proportional to the inductance and to the frequency of the current.”
AC Voltage Applied to a Capacitor – “… Comparing it to im = vm/R for a purely resistive circuit, we find that \( (1/\omega C) \) plays the role of resistance. It is called capacitive reactance and is denoted by Xc,
\( \displaystyle X_c = 1/\omega C \qquad (7.17) \)”
Resonance – “… So if \( \omega \) is varied, then at a particular frequency \( \omega_0 \), \( X_c = X_L \), and the impedance is minimum \( \left(Z = \sqrt{R^2 + 0^2} = R\right) \). This frequency is called the resonant frequency.”