LC circuits: In an LC circuit containing a 40-mH ideal inductor and a 1.2-mF capacitor, the maximum charge on the capacitor is 45 mC during the oscillations. What is the maximum current through the inductor during the oscillations?
A) 3.7 A
B) 42 A
C) 10 A
D) 6.5 A
E) 2.5 A

Question

Quizplus · Accepted Answer

We can use the formula for the maximum charge on a capacitor in an LC circuit:

Q = CV_max

where Q is the maximum charge on the capacitor, C is the capacitance, and V_max is the maximum voltage across the capacitor.

Since the capacitance is 1.2 mF and the maximum charge is 45 mC, we can solve for V_max:

V_max = Q/C = (45 × 10^-3 C) / (1.2 × 10^-3 F) = 37.5 V

Next, we can use the formula for the maximum current in an LC circuit:

I_max = V_max / (Lω)

where I_max is the maximum current through the inductor, L is the inductance, and ω is the angular frequency of the oscillations.

The angular frequency can be calculated using:

ω = 1 / sqrt(LC)

Substituting the given values, we get:

ω = 1 / sqrt((40 × 10^-3 H)(1.2 × 10^-6 F)) = 1667 rad/s

Now we can solve for the maximum current:

I_max = V_max / (Lω) = (37.5 V) / (40 × 10^-3 H)(1667 rad/s) ≈ 6.5 A

Therefore, the answer is D) 6.5 A.

LC Circuits: in an LC Circuit Containing a 40-MH Ideal