A 100-volt electromotive force is applied to an RC series circuit in which the resistance is 50 ohms and the capacitance is 10^-3 farad. Find the charge q(t) on the capacitor if q(0) = 0. Find the current i(t). Derive and solve the differential equation.
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The voltage across the resistor is given by Ohm's law as i(t)R, and the voltage across the capacitor is given by q(t)/C. Since these must add up to the total voltage, we have: i(t)R + q(t)/C = V We also know that the current i(t) is the derivative of the charge Show more…
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