A 1 microF capacitor, a 1 Ohm resistor and a 1 microH inductor are inducted in s

Question

A 1 microF capacitor, a 1 Ohm resistor and a 1 microH inductor are inducted in series with a sinusoidal signal generator of 10V peak voltage amplitude operating at a frequency of 1.0E7 rad/s.

a) Find the amplitude of current oscillation in the circuit.

b) Sketch a phasor diagram to represent this circuit. Show the phasors of all circuit elements on your diagram. Try to draw your diagram to scale.

c) Find the phase shift between the current and the generator voltage. Does the current lead the voltage or vice-versa?

Explanation / Answer

capacitance of the capacitor C = 1 F resistance of the resistro R = 1 inductance   L =   1 H maximum voltage   V = 10 V angular frequency   = 1*107 rad / s impedance of the circuit is               Z = R2 + ( XL - X C ) 2    here iunductive reactance XL = 2f L                                                  = 2 (1*107 / 2 ) ( 1*10-6 H )                                                  = 10    capacitive reactance   XC = 1/ C                                            = 0.1    there   Z = 1 + ( 10 - 0.1 ) 2                   = 9.95037       amplitude of current           I = V / Z              =   10 / 9.95037             = 1.0049 A    c) tan = ( XL - XC ) /R                  =   10 - 0.1 / 1                  =   9.9              = 84.2321 o

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