Question

a series RLC circuit has a resistance 2.50*10^2ohms, L=0.6H, capacitance=3.50*10^-6F, f=60Hz and maximum voltage=1.50*10^2V . find the:

(i) impedance

(ii)maximum current in the circuit

(iii)phase angle and its interpretation

(iv) maximum voltage across each element

Answer 1

Part A.

Inductive reactance is given by:

XL = w*L = 2*pi*f*L

XL = 2*pi*60*0.6 = 226.2 Ohm

Capacitive reactance is given by:

Xc = 1/(w*C) = 1/(2*pi*f*C)

Xc = 1/(2*pi*60*3.5*10^-6) = 757.88 ohm

Impedance is given by:

Z = sqrt (R^2 + (XL - Xc)^2)

Z = sqrt (250^2 + (226.2 - 757.88)^2)

Z = 587.5 ohm = Impedance

Part B.

Using Ohm's law:

I_max = V_max/Z

I_max = 150/587.5 = 0.255 Amp

Part C.

Phase angle is given by:

= arctan ((XL - Xc)/R)

= arctan ((226.2 - 757.88)/250)

= -64.8 deg

Interpretation: When XL < Xc, then phase angle is negative, and that means in this circuit current in leading the voltage, And Circuit is more capacitive than Inductive.

Part D.

Max Voltage across resistor will be:

Vr_max = I_max*R = 0.255*250 = 63.75 V

Max Voltage across Inductor will be:

VL_max = I_max*XL = 0.255*226.2 = 57.68 V

Max Voltage across Capacitor will be:

Vc_max = I_max*Xc = 0.255*757.88 = 193.26 V

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