Z + RC Circuit Calculator

Formulas

The formulas to calculate the total voltage and impedance in an RC series circuit are:

Total Voltage:

\[ U = \sqrt{U_R^2 + U_C^2} \]

Impedance:

\[ Z = \sqrt{R^2 + X_C^2} \]

Where:

\( U \) is the total voltage in volts (V)
\( U_R \) is the voltage across the resistor in volts (V)
\( U_C \) is the voltage across the capacitor in volts (V)
\( Z \) is the impedance in ohms (Ω)
\( R \) is the resistance in ohms (Ω)
\( X_C \) is the capacitive reactance in ohms (Ω)

What is an RC Series Circuit?

An RC series circuit is a circuit containing a resistor and a capacitor connected in series. The total voltage in the circuit is the vector sum of the voltages across the resistor and capacitor, and the impedance is the square root of the sum of the squares of the resistance and capacitive reactance.

Example Calculation

Let's assume the following values:

Voltage across Resistor (\( U_R \)): 10 V
Voltage across Capacitor (\( U_C \)): 5 V
Resistance (\( R \)): 100 Ω
Capacitive Reactance (\( X_C \)): 50 Ω

Step 1: Calculate the total voltage:

\[ U = \sqrt{10^2 + 5^2} = \sqrt{100 + 25} = \sqrt{125} \approx 11.18 \text{ V} \]

Step 2: Calculate the impedance:

\[ Z = \sqrt{100^2 + 50^2} = \sqrt{10000 + 2500} = \sqrt{12500} \approx 111.80 \text{ Ω} \]