# How a series RC circuit work?

In a series RC circuit, the alternating current through the resistor and the capacitor is the same.

The voltage VS is equal to the phasor addition of the voltage drop across the resistor (Vr) and the voltage drop across the capacitor (Vc). See the following formula: Vs = Vr + Vc. This means that when the current is maximum (peak current), it is also high in the resistor and the capacitor.

But something is different about voltages. In the resistor, the voltage and current are in phase (maximum and minimum values coincide in time). But the voltage on the capacitor is not.

As the capacitor is opposed to sudden changes in voltage, the voltage on the capacitor is delayed with respect to the current flowing through it. (the maximum voltage on the capacitor occurs after the maximum current value. (There is a difference of 90°). These 90° are equal to ¼ wavelength, given by the frequency of the current that is passing through the circuit.

The total voltage of the series RC circuit equals the voltage phasor addition of the resistor and the capacitor voltage. This voltage has a phase angle (caused by capacitor) and is obtained using the following formulas:

• Voltage value (magnitude): Vs = (VR2 + VC2)1/2.
• Phase angle O: Arctang (-VC / VR).

As stated before in a series RC circuit:

• The current leads voltage by 90 degrees in capacitor
• The current and voltage are in phase in a resistor.

Using these data we can construct the phasor diagram and the voltages triangle. With these diagrams we get the value and angle of the power supply (see above formulas).

The total resistance of the resistor-capacitor together, is called impedance (Z) and Z is the phasor addition (not an arithmetic addition) of the resistance values of the resistor and the reactance value of the capacitor. The unit of impedance is the “ohm”. The impedance (Z) is obtained using the following formula:

where:

• Vs: the magnitude of the voltage
• O1: the angle of the voltage
• I: is the magnitude of the current
• O2: the current angle.

## How is the formula used?

The impedance value (Z), is obtained dividing the voltage Vs and current I. The angle (O) is obtained substracting angle of “I” – angle “Vs”.

The same triangle voltages can be used if each value (voltage) of the triangle is dividie the current value, and thus the impedance triangle is obtained.

Note: parentheses raised to 1/2 = a square root.

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