1) The RLC circuit shown in Fig.P6.5 has R=2 ,L=0.1mH and C=40 F.The AC source p

Question

1)

The RLC circuit shown in Fig.P6.5 has R=2,L=0.1mH and C=40F.The AC source provides a voltage of amplitude 5 V and angular frequency = 25 000 rad/s.

a) Find the impedance of the circuit.

b) Suppose the current in the circuit is i = I cos(t). - Find the value of the current amplitude, I. - Write a corresponding expression for the instantaneous voltage across the source. Does the voltage lead or lag the current?

c) Find the average power dissipated by the circuit.

2) Also in Fig. P6.5 where e = 100sin(t) volts, R = 100, L = 100mH, C = 10F. Determine i(t), vR(t), vL(t), vC(t), the storage energy of the capacitor UC(t), the storage energy of the inductor UL(t), the average power of the resistor PR, the average power of the source Pe in 3 cases :

a) = 500 rad/s, b) = 100 rad/s, c) = 1000 rad/s

Explanation / Answer

Given resistance R = 2 inductance L = 0.1 mH capacitance   C = 40F maximum voltage   V = 5 V angular frrequency = 25000 rad / s inductive reactance    XL = L                                          = 25000*1*10-4                                           = 2.5 Capacitive reactance XC = 1 / C                                        = 1 / 25000*40*10-6                                         = 1 impedance of the circuit is            Z = R2 + ( XL - XC )2                 = 4 + ( 2.5 -1 ) 2                 = 2.5 amplitude of current is              I = V /Z                 = 5 / 2.5                 = 2 A   Average power dissipated               P avg   = I rms Vrms                        = I / 2   * V / 2                       =   I V /2                        = 5*2 / 2 = 5 W please post only question per one post

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