Resistor and Capacitor in AC Circuit

Let us look at the behaviour of capacitor in ac circuit.Capacitor will create opposition to current flow which is called as reactance. The reactance depends of frequency and calculated using the formula:

\[\large Xc= \frac{1}{2\pi fC}\]

In pure capacitive circuit also the voltage lags the current by 90°

In a R-C circuit the opposition to current comes from both the resistor and also from the capacitor. The combined opposition is called impedance (Z).

Analysis of R-C circuit

R1 causes opposition to current  = 5Ω

C1 causes opposition to current =\[\large Xc= \frac{1}{2\pi 60\times 100\times 10^{-6}} = 26.5\]

\[\large Z=\sqrt{R^{2}+X^{2}}\]
\[\large Z=\sqrt{5^{2}+26.5^{2}} = 26.96\]

Current in the circuit = V /Z = 100 /26.96 = 3.71A

We can find other parameters such as voltage drop across components, true power and reactive power.

Voltage drop across R

VR = IR = 3.71 x 5 = 18.55V

Voltage drop across C

VC  =IX = 3.71 x 26.5 = 98.32V

Voltage supplied ( or Total voltage) =Vector addition of VR and VC

\[\large V_{T}=\sqrt{V_{R}^{2}+V_{C}^{2}}\]

\[\large V_{T}=\sqrt{18.55^{2}+98.32^{2}} = 100\]

Try to calculate the true power and reactive power.