An LC series circuit is comprised of a 1.0-mF capacitor in series with an inductor.The period of electromagnetic oscillations in this circuit is 100 ms.What is the inductance of the inductor?
A)253 mH
B)10.0 mH
C)391 mH
D)91.3 mH

Question

Quizplus · Accepted Answer

The period (T) of electromagnetic oscillations in an LC circuit is given by $T = 2\pi\sqrt{LC}$, where L is the inductance in henries (H) and C is the capacitance in farads (F). Rearranging this formula to solve for L gives $L = \frac{T^2}{4\pi^2C}$. Substituting the given values $T = 100 \times 10^{-3} \,s$ (100 ms converted to seconds) and $C = 1.0 \times 10^{-3} \,F$ (1.0 mF converted to farads) into the formula yields $L = \frac{(100 \times 10^{-3})^2}{4\pi^2 \times 1.0 \times 10^{-3}} = \frac{10^{-2}}{4\pi^2 \times 10^{-3}} = \frac{1}{4\pi^2} \times 10^3 \approx 253 \,mH$, making option A correct.

An LC Series Circuit Is Comprised of a 1