5. Electrical circuits Exercise 1. Consider an RCL circuit where R = 2, L = C = 1. The the current I(t) is driven by an electromotive force of 2 sin 3t. The circuit equation for the voltage V(t)...

Extracted text: 5. Electrical circuits Exercise 1. Consider an RCL circuit where R = 2, L = C = 1. The the current I(t) is driven by an electromotive force of 2 sin 3t. The circuit equation for the voltage V(t) across the capacitor is d?v dv +2 dt2 + V = 2 sin 3t with V (0) = 4,V'(0) = 0. Describe the subsequent voltage oscillations 3 dt Exercise 2. An RCL circuit contains an aging battery generating E(t) = 10e t/100 volt. The resistance is 100 ohm, the inductance is 2 henry, and the capacitance is 0.001 farad. If initial charge and initial current are zero, find the charge q(t) on the capacitor for:t > 0 and sketch its graph. When does the maximum charge occur? %3D