Match List I with List II
LIST I | LIST II | ||
A. | Resistance | I. | LCR circuit |
B. | Inductance | II. | \( \displaystyle\frac{\rho l}{\pi r^{2}} \) |
C. | Capacitance | III. | \( \displaystyle\frac{\varepsilon_0 A}{d} \) |
D. | Impedance | IV. | \( \displaystyle\frac{\mu_0 N^{2} A}{L} \) |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → A-II, B-IV, C-III, D-I
Match each quantity with the expression that gives it in terms of the geometry of the component, or with the circuit in which it is defined.
(A) Resistance — this matches (II) \( \rho l/\pi r^{2} \). For a wire of length l and radius r, \( R = \rho l/A \) with area \( A = \pi r^{2} \).
(B) Inductance — this matches (IV) \( \mu_0 N^{2} A/L \). For a long solenoid of N turns, area A and length L, the self-inductance is \( \mu_0 N^{2} A/L \).
(C) Capacitance — this matches (III) \( \varepsilon_0 A/d \). For a parallel plate capacitor with plate area A and separation d in vacuum, \( C = \varepsilon_0 A/d \).
(D) Impedance — this matches (I) LCR circuit. Impedance is the effective opposition of a series LCR circuit to alternating current, \( Z = \sqrt{R^{2} + (X_L - X_C)^{2}} \).
Shortcut: The expression \( \rho l/\pi r^{2} \) is clearly the resistance of a wire, which leaves Options (2) and (3). Inductance cannot go with the “LCR circuit” entry, which is the impedance, so Option (3) is out and Option (2) remains.