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7. Electric circuits having an inductor. resistor, capacitor and an electromotive force connected in series (RLC circuits) are modeled by a differential equation analogous to the one that models the massspring oscillator. If the inductance is L (henrys). the resistance is 11', (ohms), the capacitance is (3' (farads) and the electromotive force is EU) (volts), the differential equation goveming the charge (1 (coulombs) is 1 Lij+Rd+ q : EU) C with the initial conditions given by the initial charge, q(0), and the initial current i(0) : 4(0) in the circuit Consider a circuit containing an inductor of l henry, a resistor of 100 ohms. a capacitor of 10 4 farads driven by an electromotive force of EU) 962 sin 605 volts. (a) Write the differential equation governing the charge in the circuit. (b) Find the general solution of the differential equation in pan (a). (c) For the differential equation in part (a), nd the particular solution to the initial value problem if there is no current and no charge in the circuit at time t 0. (d) Find the value of the steady state charge and steady state current [i(t) : 120)] when t : 7r /60 seconds