Question

Consider the following LRC-series circuit.

L = 1 h, R = 100 Ω, C = 0.0004
f, E(t) = 40 V, q(0) = 0 C, i(0) =
3 A
Find the general solution for charge q(t) on
the capacitor.
q(t) = _____ C
Find t

Answer 1

The general solution for the charge q(t) on the capacitor in an LRC series circuit can be represented by an underdamped exponential cosine function. The exact form requires applying the initial conditions to the circuit's differential equation.

Step-by-step explanation:

The question at hand is asking for the general solution for the charge q(t) on the capacitor in a given LRC series circuit. Due to the nature of this circuit and the initial conditions provided, we will use the underdamped solution of the second-order differential equation that governs an LRC circuit. The charge q(t) can be found using the following expression: q(t) = Q0 e-Rt/(2L) cos(ωt + φ), where Q0 is the initial charge, R is the resistance, L is the inductance, ω is the angular frequency, t is time, and φ is the phase constant. The frequency ω can be calculated from the inductance L and the capacitance C. However, to find the exact form of q(t) including constants like Q0 and φ, one must apply the given initial conditions, which would typically involve solving a set of simultaneous equations that arise from the circuit's differential equation.