The natural response of an RLC circuit is described by the differential equation
The v(t) is
The differential equation for the circuit shown in fig. P1.6.2. is
The differential equation for the circuit shown in fig. P1.6.3 is
In the circuit of fig. P.1.6.4 vs = 0 for t > 0. The initial condition are v(0) = 6 V and dv(0) dt = 3000 Vs. The v(t) for t > 0 is
A + B = 6, 100 A  400B = 3000 ⇒ B = 8, A = 2
The circuit shown in fig. P1.6.5 has been open for a long time before closing at t = 0. The initial condition is v(0) = 2 V. The v(t) for t > is
The characteristic equation is
After putting the values, s^{2} +4s + 3 = 0
Circuit is shown in fig. P.1.6. Initial conditions are i_{1}(0) = i_{2}(0) = 11A
Q. i_{1} (1 s) = ?
In differential equation putting t = 0 and solving
Circuit is shown in fig. P.1.6. Initial conditions are i_{1}(0) = i_{2}(0) = 11A
Q. i_{2} (1 s) = ?
v_{C}(t) = ? for t > 0
The circuit shown in fig. P1.6.9 is in steady state with switch open. At t = 0 the switch is closed. The output voltage v_{C}(t) for t > 0 is
The switch of the circuit shown in fig. P1.6.10 is opened at t = 0 after long time. The v(t) , for t > 0 is
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