Question

A 230v, 50 Hz, is applied a series connected resistor 30 ohms and inductor 0.5mH, than find X_L, current through the circuit, voltage across each component, and also draw phasor diagram between current and voltage.

Answer 1

Explain the behavior of AC through RC Series Circuit:

Consider an AC circuit with a resistance R and a capacitance C connected in series as shown in the figure. The alternating voltage v is given by

  \(v=v_{m}sin(\omega t)\)

The current flowing in the circuit is i. The voltage across the resistor is V_R and that across the capacitor is V_c

V_{R =} IR is in phase with I

V_c = IX_c lags current by 90 degrees

With the above information, the phasor diagram can be drawn as shown

The current I is taken as the reference phasor. The voltage VR is in phase with I and the voltage VC lags behind the current by 90⁰. The resultant voltage V can be drawn as shown in the figure. From the phasor diagram we observe that the voltage lags behind the current by an angle Φ or in other words the current leads the voltage by an angle Φ.

The waveform and equations for an RC series circuit can be drawn as below.

From the phasor diagram, the expressions for the resultant voltage V and the angle Φ can be derived as follows.

Where impedance \(Z=\sqrt{R^2+{X_{c}}^2}\)

The impedance in an AC circuit is similar to a resistance in a DC circuit. The unit for impedance is ohms(Ω).

Phase angle:

Impedance triangle:

Phasor algebra for RC series circuit.