Question

Find the charge qᵗ on the capacitor and the current iᵗ in

the given LRC-series circuit. L = 5 2 h, R = 10 Ω, C = 1 20 f, Eᵗ
= 400 V,
qᵗ = _____ C,
iᵗ = ______ A
Find the maximum charge on the capacitor

Answer 1

To find the charge and current in the LRC-series circuit, use the formulas q = CV and i = dq/dt. For the given values L = 5 2 H, R = 10 Ω, C = 1 20 F, and Eᵗ= 400 V, the charge qᵗ on the capacitor is 20 C and the current iᵗ is (1/20 F) * (400 V / 52 H) * sin(ωt).

Step-by-step explanation:

To find the charge and current in the given LRC-series circuit, we can use the formulas q = CV and i = dq/dt. Given the values L = 52 H, R = 10 Ω, C = 1/20 F, and E = 400 V, we can substitute these values into the formulas to find the charge and current.

First, we calculate the charge: q = CV = (1/20 F)(400 V) = 20 C. So, the charge qᵗ on the capacitor is 20 C.

Next, we calculate the current: i = dq/dt = d(CV)/dt = C * dV/dt = C * (E / L) * sin(ωt), where ω = 1/sqrt(LC). Plugging in the values, we get iᵗ = (1/20 F) * (400 V / 52 H) * sin(ωt).