The figure shows a circuit containing an electromotive force, a capacitor with a capacitance of C farads (F), and a resistor with a resistance of R ohms (Ω). The voltage drop across the capacitor is Q / C, where Q is the charge (in coulombs), so in this case Kirchhoff's Law gives
RI + Q / C = E(t)
But I = dQ / dt, so we have
R dQ/ dt + 1 / C Q = E(t)
Suppose the resistance is 5 Ω, the capacitance is 0.05 F, a battery gives a constant voltage of 60 V, and the initial charge is Q(0) = 0 C. Find the charge and the current at time t.

Transcribed Image Text:

C E R