Question: 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
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 Kirchhoffs Law gives Rl + Q/C = E(t) But l + dQ/dt (see Example 3 in Section 3.3), so we have Suppose the resistance is 5Ω, 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.
(E
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dQ dt 20Q 60 with Q0 0 C Then the integrating factor is el ... View full answer
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