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
But I= dQ/dt (see Example 3.7.3), so we have
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.
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Calculus: Early Transcendentals
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