Electronics - Capacitors - Discussion

Power factor is the ratio of True power to the Volt-Ampere power.

When the circuit is pure resistive: true power = VA power.

With reactance : Reactive power comes into picture (VA power increases).

Which means impact of reactance in the circuit. This factor of increase in the Power is determined with concept of power factor.

In pure Resistive circuits: V and I are in same phase.

With Reactance : Phase lead/lag occurs (phase difference).

So, cosine of phase difference (cos°) which is literally equivalent to R/Z from co ordinate system (real and imaginary axis).

Given: f = 1.1 kHz; VAC = 5V; R = 50Ω ; C = 5.6μ F.

XC = 1/ (2 * π * F * C).
XC = 1 / (2 * 3.14 * 1.1 * 103 * 5.6 * 10-6)
XC = 1 / 38.6848 * 10-3,
XC = 0.02584 * 10-3,
XC = 25.84.

The phase angle between the current and voltage is calculated from the impedance triangle above as:

For RC Circuit; tan (θ) = XC / R,
(θ) = tan-1 (XC / R),
(θ) = tan-1 (25.84/50),
(θ) = tan-1 (0.5168).

(θ) = 30.02˚.

For RC circuit, tan θ = -Xc/R
Xc=1/(2*3.14*(1.1*10^3)*(5.6*10^-6) =0.0258*10^3
also we have R=50 ohm

=> tan θ= -0.516
θ = tan-1 (-0.516)= -27.29 or -27.3

We know tthat cos(angle)=Xc/R

Xc=(1/2*pi*f*c)

By substituting values will get cos(angle)=0.355

So angle=27.3

But in capacitor power factor is lagging so ans is -27.3

z= R+X
X=1/j*2*pi*f*c = -j*25.83
SO, z= R-j(1/2*pi*f*c) = 50-j*25.83

tan(angle)= img. part/ real part
= -25.83/50
angle = -27.32 degrees

@Kiran

Don't divide (XC/R) and calculate phase angle.

Calculate directly using (θ) = tan-1 (-XC / R).
You will get (θ) = -27.32˚.

Theata = tan-1(1/wrc).
So Ans = 27.3 degree.

Sign is +ve because:
Current leads the voltage by 90 degree.

In capacitor : Current lead the voltage by 90.

In Inductor: Voltage leads the current by 90.

Z = R+jX, so tanθ = X/R X = 1/2PIfc place the given values in following equation.

In capacitor lead the voltage by 90 degree in inductor voltage lead the current by 90.