Introduction: RC Circuits

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RC circuits

  • Impedance: is what the source “Sees” as total Opposition to Current.

The method of calculation of impedance differs from one circuit

Step 1:

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

Step 2:

  • 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.

Step 3: Voltage and Current Phasor Diagram for the Waveforms

Step 4: Current, Resistance and Voltage Phase Angles of Series RC Circuits

Step 5: 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:
Itot = Vs/Z Z = Vs/Itot Vs = Itot * Z

Also don’t forget:

Xc=1/2πFC

Step 6: Variation of Impedance With Frequency

Step 7: Variation of Impedance and Phase Angle With Frequency

Step 8: An Illustration of How Z and XC Change With Frequency

R remains constant

Step 9: Circuit on Kicad

Step 10: Simulation on Kicad