Calculate RC Series Circuit

Calculator and formulas for calculating the voltage and power of an RC series circuit

RC Series Circuit Calculator

RC Series Circuit

This function calculates the voltages, powers, current, apparent and reactive resistance of a series connection of a resistor and a capacitor.

Results
Reactance XC:
Total Resistance Z:
Voltage UR:
Voltage UC:
Current I:
Active Power P:
Reactive Power Q:
Apparent Power S:
Phase Angle φ:

RC Series Circuit

CR Series Circuit, RC Series Circuit
Series Circuit Properties
  • Same current through all components
  • Total voltage is the sum of the partial voltages
  • Impedance greater than the largest individual resistance
  • Phase shift between voltages
Basic Formulas
\[U=\sqrt{U_R^2+U_C^2}\] \[Z=\sqrt{R^2+X_C^2}\]

Voltage and resistance triangle according to Pythagoras

Power Triangle
\[S=\sqrt{P^2+Q^2}\]
  • P: Active power (in the resistor)
  • Q: Reactive power (in the capacitor)
  • S: Apparent power (total power)

RC Series Circuit - Theory and Formulas

Basics of the RC Series Circuit

The total resistance of the RC series circuit in AC is called apparent resistance or impedance Z. Ohm's law applies to the entire circuit. The current is the same at every measuring point. In the ohmic resistor, current and voltage are in phase. In the capacitive reactance of the capacitor, the voltage lags the current by −90°.

Voltage Triangle

Voltages
\[U=\sqrt{U_R^2+U_C^2}\] \[\phi=\arctan\left(\frac{U_C}{U_R}\right)\]
U = Total voltage
UR = Voltage across resistor
UC = Voltage across capacitor
Impedance Triangle
\[Z=\sqrt{R^2+X_C^2}\]
R = Resistance
XC = Reactance
Z = Total resistance (impedance)

Powers in the RC Series Circuit

The multiplication of the instantaneous values of voltage U and current I gives the power curve.

Active Power
\[P=U_R \cdot I\] \[P=R \cdot I^2\]

The active power is converted to heat in the resistor.

Reactive Power
\[Q=U_C \cdot I\] \[Q=X_C \cdot I^2\]

The reactive power oscillates between the capacitor and the generator.

Apparent Power
\[S=U \cdot I\] \[S=Z \cdot I^2\]

The apparent power is a purely mathematical quantity.

Power Triangle

Power Relationships
\[S=\sqrt{P^2+Q^2}\] \[\phi=\arctan\left(\frac{Q}{P}\right)\]
\[\cos(\phi)=\frac{P}{S}\]

Power factor cos(φ)

Power Factor cos(φ)

Power Factor
\[\cos(\phi)=\frac{P}{S}\]

The power factor indicates how much of the apparent power S is converted as active power P. The closer cos(φ) is to 1, the more efficient the energy transfer.

S = Apparent power
P = Active power
φ = Phase shift

Practical Applications

Filter Circuits:
• Low-pass filter
• High-pass filter
• Band-pass filter
• Crossovers
Timing Circuits:
• RC oscillators
• Timers
• Delay circuits
• Pulse generators
Coupling:
• AC coupling
• Amplifier coupling
• DC decoupling
• Signal transmission

Phase Behavior

Phase Shift
  • Resistor: Current and voltage in phase (φ = 0°)
  • Capacitor: Voltage lags current by -90°
  • Total circuit: Phase angle between 0° and -90°
  • Capacitive: For XC > R, the circuit is capacitive
  • Resistive: For R > XC, the ohmic character dominates

Frequency Dependence

Low Frequencies
  • XC is large
  • Impedance is dominated by XC
  • Large phase shift
  • Capacitor acts as a block
High Frequencies
  • XC is small
  • Impedance is dominated by R
  • Small phase shift
  • Capacitor acts as a short circuit

Design Guidelines

Important Design Aspects
  • Voltage distribution: Depends on frequency and component values
  • Resonance: At f = fg, Z is minimal
  • Voltage withstand: Partial voltages can be greater than total voltage
  • Loss factor: Real capacitors have additional ESR
  • Tolerances: Component variations affect behavior
  • Temperature effect: Capacitance and resistance are temperature dependent

Is this page helpful?            
Thank you for your feedback!

Sorry about that

How can we improve it?


Capacitor functions

Series connection with capacitors  •  Series connection with 2 capacitors  •  Reactance Xc of a capacitor  •  Time constant of an R/C circuit  •  Capacitor charging voltage  •  Capacitor discharge voltage  •  R/C for the charging voltage  •  Series circuit R/C  •  Parallel circuit R/C  •  Low pass-filter R/C  •  High pass-filter R/C  •  Integrator R/C  •  Differentiator R/C  •  Cutoff-frequency R,C  •  R and C for a given impedance  •