An LC series circuit is comprised of a capacitor in series with a 40 mF inductor.The period of electromagnetic oscillations in this circuit is 100 ms.What is the capacitance of the capacitor?
A)12.1 mF
B)14.2 mF
C)6.33 mF
D)1.00 mF

Question

Quizplus · Accepted Answer

The period $T$ of electromagnetic oscillations in an LC circuit is given by the formula $T = 2\pi\sqrt{LC}$, where $L$ is the inductance in henries (H) and $C$ is the capacitance in farads (F). Rearranging the formula to solve for $C$, we get $C = \frac{T^2}{4\pi^2L}$.Given that $T = 100 \, \text{ms} = 0.1 \, \text{s}$ and $L = 40 \, \text{mF} = 40 \times 10^{-3} \, \text{H}$, we can substitute these values into the formula:$$C = \frac{(0.1)^2}{4\pi^2 \times 40 \times 10^{-3}}$$$$C = \frac{0.01}{4\pi^2 \times 40 \times 10^{-3}}$$$$C = \frac{0.01}{4 \times (9.8696) \times 40 \times 10^{-3}}$$$$C = \frac{0.01}{1.25664}$$$$C \approx 6.33 \times 10^{-3} \, \text{F} = 6.33 \, \text{mF}$$Therefore, the capacitance of the capacitor is approximately 6.33 mF.

An LC Series Circuit Is Comprised of a Capacitor in Series