RC Circuits

RC circuits
- Impedance: is what the source “Sees” as total Opposition to Current.
The method of calculation of impedance differs from one circuit

When a circuit is purely capacitive(contains capacitor only), the phase angle between applied voltage and total current is 90 ° (Current Leads)

- When there is a combination of both resistance and capacitance in a circuit, the phase angle between resistance (R) and capacitive reactance (XC ) is 90 ° and the phase angle for total impedance (Z) is somewhere between 0 ° and 90 °.
- When there is a combination of both resistance and capacitance in a circuit, the phase angle between total current (I T) and the capacitor voltage (V C) is 90 ° and the phase angle between the applied voltage (VS ) and total current (I T ) is somewhere between 0 ° and 90 ° , depending on relative values of resistance and capacitance.
Voltage and Current Phasor Diagram for the Waveforms

Current, Resistance and Voltage Phase Angles of Series RC Circuits

Impedance and Phase Angle of Series RC Circuits

- In the series RC circuit, the total impedance is the phasor sum of R and Xc
- Impedance magnitude: Z = √ R^2 + Xc^2 (Vector sum)
- Phase angle: θ = tan-1(X C/R)
Why do we use vector sum not algebraic sum ?
Ans: Because Resistance doesn’t delay the voltage, but the Capacitor do that.
So, Z=R+Xc is wrong.
- The application of Ohm’s law to an entire series RC circuit involves the use of the quantities Z, Vs, and Itot as:
Also don’t forget:
Xc=1/2πFC
Variation of Impedance With Frequency

Variation of Impedance and Phase Angle With Frequency

An Illustration of How Z and XC Change With Frequency

R remains constant
Circuit on Kicad

Simulation on Kicad
