We have seen that in a series RLC circuit, Kirchoff's voltage law (VR+VL+Vc = Vs, where Vs is the supply voltage) leads to a 2nd order differential equation for the current I(t). Let us now consider a parallel RLC circuit consisting of a 5 H inductor, a 10 F capacitor, and a 0 s, there is a supply current Is of 5 A. The supply voltage Vs is common to all three components. Kirchoff's current law states that IR+ IL + Ic = Is. 0.5 N resistor. At timet =

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3. We have seen that in a series RLC circuit, Kirchoff's voltage law (VR +VL + Vc = Vs, where
Vs is the supply voltage) leads to a 2nd order differential equation for the current I(t). Let
us now consider a parallel RLC circuit consisting of a 5 H inductor, a 10 F capacitor, and a
0.5 N resistor. At time t = 0 s, there is a supply current Is of 5 A. The supply voltage Vs is
common to all three components. Kirchoff's current law states that IR + IL + Iç = Is.
Transcribed Image Text:3. We have seen that in a series RLC circuit, Kirchoff's voltage law (VR +VL + Vc = Vs, where Vs is the supply voltage) leads to a 2nd order differential equation for the current I(t). Let us now consider a parallel RLC circuit consisting of a 5 H inductor, a 10 F capacitor, and a 0.5 N resistor. At time t = 0 s, there is a supply current Is of 5 A. The supply voltage Vs is common to all three components. Kirchoff's current law states that IR + IL + Iç = Is.
Is
A
IR
IL
Ic
Vs
+
R
(a) Construct a 2nd order differential equation for Vs using Kirchoff's current law and the
voltage-current relationships for each of the three components discussed in this week's
slides.
(b) Solve the differential equation, including considering appropriate boundary conditions,
to verify that Vs = 5e-0.1t sin (0.1t).
Transcribed Image Text:Is A IR IL Ic Vs + R (a) Construct a 2nd order differential equation for Vs using Kirchoff's current law and the voltage-current relationships for each of the three components discussed in this week's slides. (b) Solve the differential equation, including considering appropriate boundary conditions, to verify that Vs = 5e-0.1t sin (0.1t).
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