With R,L and C connected is series across an ac Voltage source (Vs) the current through each component is equal to the source current (i) and in phase with the source current. Therefore the Voltage drop across each component is equal to the source current times the complex impedance of the component. Therefore with reference to the source Voltage the Voltage developed across the inductor (VL) is advanced 90`, the Voltage developed across the capacitor (Vc) is delayed 90` and the Voltage developed across the resistor (Vr) is left at 0 degrees. Since the Voltage across the capacitor is exactly 180` out of phase with the Voltage across inductor the net reactive Voltage equals VL - Vc = Vx and the sum of the Voltage drops around the circuit is equal to zero Volts.
[(Vof source)*(cos 0`)] - {[(Vr)*(cos 0`)] + [(V of inductor) + (-V of capacitor)]*[cos arc tan (X/R)]} = 0V
There are several different configurations that constitute an "RLC circuit": all in series, all in parallel, or various combinations of series / parallel. So I can't be too specific; I can only talk in general and conceptual terms. The basic Kirchoff's Laws still apply, but you need to take into account the phase of the voltages across each component, or the phase of the currents - depending on which Law you're using. Also, bear in mind that any coil will also have a resistance component and if it is not an air-cored coil, the effects of its core will need to be factored in too.
Kirchoff's Laws apply to all circuits, so this shouldn't be confusing. You can write either the applicable differential equations, or for a circuit with an AC excitation, you can write the phasor equations. They both will work.
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With R,L and C connected is series across an ac Voltage source (Vs) the current through each component is equal to the source current (i) and in phase with the source current. Therefore the Voltage drop across each component is equal to the source current times the complex impedance of the component. Therefore with reference to the source Voltage the Voltage developed across the inductor (VL) is advanced 90`, the Voltage developed across the capacitor (Vc) is delayed 90` and the Voltage developed across the resistor (Vr) is left at 0 degrees. Since the Voltage across the capacitor is exactly 180` out of phase with the Voltage across inductor the net reactive Voltage equals VL - Vc = Vx and the sum of the Voltage drops around the circuit is equal to zero Volts.
[(Vof source)*(cos 0`)] - {[(Vr)*(cos 0`)] + [(V of inductor) + (-V of capacitor)]*[cos arc tan (X/R)]} = 0V
X in the above equation = XL - Xc
There are several different configurations that constitute an "RLC circuit": all in series, all in parallel, or various combinations of series / parallel. So I can't be too specific; I can only talk in general and conceptual terms. The basic Kirchoff's Laws still apply, but you need to take into account the phase of the voltages across each component, or the phase of the currents - depending on which Law you're using. Also, bear in mind that any coil will also have a resistance component and if it is not an air-cored coil, the effects of its core will need to be factored in too.
Kirchoff's Laws apply to all circuits, so this shouldn't be confusing. You can write either the applicable differential equations, or for a circuit with an AC excitation, you can write the phasor equations. They both will work.