Calculate RC series circuit
Calculator and formulas for calculating the voltage and power of an RC series circuit
This function calculates the voltages, powers, currents, impedance and reactance of a series circuit consisting of a resistor and a capacitor.
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Formula for calculating a series circuit
The total resistance of the RC series circuit in the AC circuit is called Impedance Z. Ohm's law applies to the entire circuit.
The current is the same at every measuring point. Current and voltage are in phase at the ohmic resistance. The voltage rushes across the capacitive reactance of the capacitor after the current by −90 °.
The total voltage U is the sum of the geometrically added partial voltages. For this purpose, both partial voltages form the legs of a right triangle. Its hypotenuse corresponds to the total voltage U. The resulting triangle is called the voltage triangle or vector diagram of the voltages.
Voltage triangle
\(\displaystyle U=\sqrt{{U_R}^2+{U_C}^2} \) \(\displaystyle φ=arctan \left( \frac{U_C}{U_R} \right) \)
\(\displaystyle U\) Total voltage \(\displaystyle U_R\) Voltage across the resistor \(\displaystyle U_C\) Voltage across the capacitor
Resistance triangle
\(\displaystyle Z=\sqrt{R^2+{X_C}^2} \)
\(\displaystyle R\) Real power \(\displaystyle X_C\) Reactance \(\displaystyle Z\) Impedance
Power triangle
\(\displaystyle S=\sqrt{P^2+Q^2} \) \(\displaystyle φ=arctan \left( \frac{Q}{P} \right) \)
\(\displaystyle P\) Real power \(\displaystyle Q\) Reactive power \(\displaystyle S\) Apparent power
Power in the RC series circuit
The multiplication of the instantaneous values of voltage U and current I results in the power curve.
Real power
The multiplication of the voltage across the resistor and the current result in the real power. The real power is converted into heat in the resistor.
\(\displaystyle P=U_R·I \) \(\displaystyle P=R·I^2 \)
Reactive power
The reactive power oscillates back and forth between the capacitor and the generator.
\(\displaystyle Q=U_C ·I \) \(\displaystyle Q=X_C ·I^2 \)
Apparent power
The apparent power is a purely arithmetic variable.
\(\displaystyle S=U ·I \) \(\displaystyle S=Z ·I^2 \)
Leistungsfaktor cos(φ)
The power factor indicates how much of the apparent power S is the real power P is generated.
\(\displaystyle cos(φ)=\frac{P}{S} \)
\(\displaystyle S\) Apparent power \(\displaystyle P\) Real power \(\displaystyle φ\) Phase shift
Capacitor functions
Series connection with capacitorsSeries 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
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