PROBLEM 34E

RLC Series Circuit. In the study of an electrical circuit consisting of a resistor, capacitor, inductor, and an electromotive force (see Figure 4.9), we are led to an initial value problem of the form

where L is the inductance in henrys, R is the resistance in ohms, C is the capacitance in farads, E(t) is the electromotive force in volts q(t), is the charge in coulombs on the capacitor at time t, and I = dq/ dt is the current in amperes. Find the current at time t if the charge on the capacitor is initially zero, the initial current is zero, L = 10 H, R = 20 Ω, C = (6262)-1 F, and E(t) = 100 (V. [Hint: Differentiate both sides of the differential equation in (20) to obtain a homogeneous linear second-order equation for I(t). Then use (20) to determine dI/dt at t = 0.]

Solution:

Step 1:

In this problem, we have to find the current at time t if the charge on the capacitor is initially zero.