What is R-L-C series connection for A.C. circuit ? Explanation

Question: Explain R-L-C series connection for A.C. circuit ?

Resistance – Inductance – Capacitance (RLC) series circuit

Resistance of R ohms, inductance of L henries and capacitance of C farads connected in series, as shown in figure (a). Let, the current flowing through the circuit be of I amperes and supply frequency be  f Hz.

Let, the current flowing through the circuit be of I amperes and supply frequency be  f Hz. Voltage drop across resistance, VR = IR in phase With I.

Voltage drop across inductance-

Voltage drop across capacitance-

VC and VL out of phase with each other (or reverse in phase), therefore, when combined by parallelogram they cancel each other. The circuit can either be effectively Inductive or capacitive depending upon which voltage drop (VC or VL) is predominant. Let, us consider the case when when VL is greater than VC.

The applied voltage V, being equal to the phasor sum of VR , VC and VL is given in magnitude by-

is known as Impedance of the circuit and is represented by Z. Its unit is ohm. Phase angle between voltage and current is given Φ between voltage and current is given By-

The angle

 Φ will be + ve i.e. applied voltage will Iead the current if XL  >  XC  and will be  – ve  i.e. voltage will be behind the current if   XL   <  XC Power factor of the circuit is given by ,

Power consumed in the circuit, P =I2 R VI cos Φ

Reactance, Inductive reactance, XL  is directly proportional to frequency being equal to wL or 2πfL and capacitive reactance, Xc is inversely proportional I frequency being equal to

Inductive reactance causes the current to lag behind the applied voltage, while the capacitive reactance causes the current to lead the voltage. So when inductance and capacitance arc connected in series, their effects neutralize each other and their combined effect is then their difference. The combined effect of inductive reactance and capacitive reactance is called the reactance and is found by subtracting the capacitive reactance from the inductive reactance or according to equation.

When XL > Xc i.e. XL —Xc is positive, the circuit is inductive and phase angle Φ is positive. When XL < Xc i.e. XL —Xc is negative, the circuit is capacitive and phase angle Φ is negative. When XL = Xc i.e. X la —Xc = 0, the circuit is purely resistive and phase angle Φ is zero.

If the expression for applied voltage is taken as v = V max sin πt

Then expression for the current will be max sin (cot ± Φ) where,

The value Of will be positive when current lead i.e. when Xc > XL  and negative when current lags i.e. when    XL  >  XC.


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