First Order Linear ODE The RC circuit shown in Figure 1 below depicts the discha

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First Order Linear ODE

The RC circuit shown in Figure 1 below depicts the discharging cycle of the capacitor C through the resistor R. Figure 1: Discharging cycle of a RC circuit Obtain the general differential equation of this RC circuit. Obtain the general solution of the differential equation (basically the charge) given R=5Ohm and C=0.05F. Obtain a particular solution given the initial charge Q(0)=1 Coulomb. Use your knowledge of circuit theory to obtain the general differential equation that represents the givencircuit. Remember that the voltage drop across a capacitor is given by V=Q/C where Q is the charge in Coulombs and C is the capacitance in Farads. Also, current I is defined as the rate of change of charge i.e., l = dQ/dt. R dQ/dt + QC = 0 Q = c1e4t Q = e4t CdQ/dt + Q/R = 0 Q = c1e-4t Q = e-4t 1/C dQ/dt + RQ = 0 Q = c1e-4/4 Q = e-t/4 None of the above: see Problem Work

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answer is (a)

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