Home | | **Physics 12th Std** | AC circuit containing a resistor, an inductor and a capacitor in series - Series RLC circuit

Consider a circuit containing a resistor of resistance R, a inductor of inductance L and a capacitor of capacitance C connected across an alternating voltage source.

**AC circuit containing**** ****a resistor, an inductor
and a capacitor in series - Series RLC circuit**

Consider a circuit
containing a resistor of resistance *R*, a inductor of inductance *L*
and a capacitor of capacitance *C* connected across an alternating voltage
source (Figure 4.51). The applied alternating voltage is given by the equation.

Let i be the resulting
circuit current in the circuit at that instant. As a result, the voltage is
developed across R, L and C. We know that voltage across R (V_{R}) is
in phase with i, voltage across L (V_{L}) leads i by Ï€/2 and voltage
across C (V_{C}) lags i by Ï€/2.

The phasor diagram is drawn with current as the reference phasor. The current is represented by the phasor

as shown in Figure 4.52.

The length of these
phasors are

OI = I_{m}, OA =
I_{m}R, OB = I_{m}X_{L}; OC = I_{m}X_{C}

The circuit is either
effectively inductive or capacitive or resistive that depends on the value of *V _{L}*
or

By parallelogram law,
the diagonal * *gives the resultant voltage* Ï… *of* V _{R}
*and

*Z *is called impedance of
the circuit* *which refers to the effective opposition to the circuit
current by the series *RLC* circuit. The voltage triangle and impedance
triangle are given in the Figure 4.53.

From phasor diagram, the
phase angle between *Ï…* and *i* is found out from the following
relation

**Special cases**

(i) If *X _{L}*
>

âˆ´
Ï… = *V _{m}* sin Ï‰

(ii) If *X _{L}*
<

âˆ´ Ï…
= *V _{m}* sin Ï‰

(iii) If *X _{L}*
=

âˆ´
Ï… =*V _{m}* sin Ï‰

Tags : Phasor diagram, Circuit Diagram, Formula, Solved Example Problems | Alternating Current (AC) , 12th Physics : Electromagnetic Induction and Alternating Current

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12th Physics : Electromagnetic Induction and Alternating Current : AC circuit containing a resistor, an inductor and a capacitor in series - Series RLC circuit | Phasor diagram, Circuit Diagram, Formula, Solved Example Problems | Alternating Current (AC)

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