(a) Consider a series resistor–inductor circuit with L = 2H, R = 10, and an applied EMF of E = 100 sin(t). Use an integrating factor to solve the differential equation, and find the current in the circuit after 0.2 second given that I (0) = 0.

(b) The differential equation used to model a series resistor–capacitor circuit is given by R

dQ dt +

Q C = E, where Q is the charge across the capacitor. If a variable resistance R = 1/(5 + t) and a capacitance C = 0.5 F are connected in series with an applied EMF, E = 100V, find the charge on the capacitor given that Q(0) = 0.