The simplest RC circuit consists of resistors and capacitors connected in series and powered by a common voltage source. Due to the series connection of capacitors and resistors, the same current flows through them. The voltage on capacitor VC and resistor VR are perpendicular to each other in the diagram. Their total sum is always greater than the total voltage of V.
The vector diagram of a series resonant RC circuit shows that the total current lags behind the total voltage by an angle of 0 to 90 degrees. Please note that if you short circuit the resistor, the angle will be 90 ° (pure resistive load), and if you short circuit the capacitor, the angle will be 0 ° (pure active load).
The impedance of a series resonant RC circuit looks like the upper figure in a vector diagram, where the active resistor R is on the horizontal axis and the reactance X C is on the vertical axis. The hypotenuse of the generated right angled triangle is the impedance of the circuit, and the phase angle is the angle between the horizontal axis and the impedance vector.
The phase angle range varies from 0 ° for pure resistive circuits to -90 ° for pure capacitive circuits. From the stress triangle, we obtain:
Determine the phase angle using the inverse function (tangency):
In a series RL circuit, the same current flows through the coil and resistor. The voltage on coil VC lags behind the total current by 90 °, and the voltage on the resistor is in phase with the current. According to Kirchhoff's second law (for voltage), the sum of voltage drops across circuit components must be equal to the total voltage VT. The voltage on resistor VR and capacitor VC is 90 ° out of phase, so they are added together using a vector diagram, and the total voltage is determined by the following formula:
Please note that the total voltage is always less than the sum of the voltage drops across the resistor and coil, just like the hypotenuse of a right angled triangle is always less than the sum of the legs.