Match List – I with List – II.
| List - I | List - II | ||
|---|---|---|---|
| (A) | L.C. Oscillation | (I) | Inductor supplied with AC |
| (B) | \( Q=\displaystyle\frac{\omega_0 L}{R} \) | (II) | \( \displaystyle\frac{d^{2}q}{dt^{2}}+\frac{1}{LC}q=0 \) |
| (C) | Voltage leads current | (III) | \( \displaystyle\frac{i_p}{i_s}=\frac{V_s}{V_p} \) |
| (D) | Transformer | (IV) | Sharpness of resonance curve |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(II), (B)-(IV), (C)-(I), (D)-(III)
(A) L.C. Oscillation — this matches (II) \( \frac{d^{2}q}{dt^{2}}+\frac{1}{LC}q=0 \). The charge on the capacitor of an LC circuit obeys this equation, which is the equation of simple harmonic motion with \( \omega_0 = 1/\sqrt{LC} \).
(B) \( Q=\omega_0 L/R \) — this matches (IV) Sharpness of resonance curve. This is the quality factor of a series resonant circuit; the larger it is, the sharper the resonance.
(C) Voltage leads current — this matches (I) Inductor supplied with AC. In a pure inductor the voltage leads the current by \( \pi/2 \).
(D) Transformer — this matches (III) \( \frac{i_p}{i_s}=\frac{V_s}{V_p} \). For an ideal transformer the power in the primary equals that in the secondary, so \( V_p i_p = V_s i_s \).