Question

40 240 mH 1.0) 2.5 mFPart A Find the steady-state expression for io(t) in the circuit in (Figure 1) if U, = 150 sin 50t mV. Suppose that i(t) = Io

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Answer #1

Here, the input voltage

vs = 150sin(50t) mV

comparing this to standard representation of vs = Vmsin(wt)

We get,

w = 50 rad/s

Now,

Resistance, R = 4 ohms

Inductive reactance, XL = j(wL) = j( 50 * 240 * 10-3) = j12 ohms

Capacitive reactance, XC = -j(1/wC) = -j(1/50*2.5*10-3) = -j8 ohms

So, total impedance of the circuit

Z = R+j(XL-XC) = (4 +j 4) ohms

So, the current flowing through the circuit

150 sin(50+) io(t) = vs/Z = = 4+24

i.(t) = 26.52 sin(50t – 45) = 26.52cos(50t – 45 – 90)

i.(t) = 26.52cos(50t – 135)

So,

Io = 26.52mA

w = 50 rad/s

\phi = -135 deg

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