Question

(In a few sentences)

For An RLC Circuit

1) describe the relationship between the frequency amplitude and phase shift.

ex. as the frequency increases the phase shift....

for an RC circuit

1) desribe the relationship between the capacitance, the pahse shift and the current

Answer 1

In a series RLC circuit, current I is given by I = where, Z is the total impedance of the circuit.

Z = R + j(X_L-X_C) where, X_L ( = 2*pi*f*L) is the inductive reactance and X_C ( = 1/2*pi*f*C) is the capacitive reactance.

We know that at low freqency X_C>>X_L , therefore, intially circuit behaves as a RC circuit, therefore, we the current leads the voltage and hence phase shift is negative ( Since phase angle is always calculated as angle of voltage - angle of current) . At Resonance Frequency X_L=X_c therefore circuit behaves a purely resistive circuit. Hence, the phase shift between voltage and current is zero. At frequency greater than Resonance Frequency, X_L>>X_C , therefore, current lags the voltage and hence phase shift is positive.

2. For an RC circuit, I = , where, Z = R-jX_C.

We can here see that I always leads V by angle theta which is equal to tan^-1(X_c/R). Now since X_C = 1/2*pi*f*C, therefore, as frequency increases theta becomes smaller.