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, V_{R} = IR in phase With I.

Voltage drop across inductance-

Voltage drop across capacitance-

V_{C} and V_{L} 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 (V_{C} or V_{L}) is predominant. Let, us consider the case when when VL is greater than V_{C}.

The applied voltage V, being equal to the phasor sum of V_{R }, V_{C} and V_{L} 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 X_{L} > X_{C} and will be – ve i.e. voltage will be behind the current if X_{L} < X_{C} Power factor of the circuit is given by ,

Power consumed in the circuit, P =I^{2 }R VI cos **Φ**

**Reactance**, I**nductive** **reactance**, X_{L} is directly proportional to frequency being equal to wL or 2**π**fL 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 **π**t

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 X_{L} > X_{C}.

## A.C. CIRCUITS TOPIC

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- Phasor representation of alternating quantities – resistive, inductive, capacitive
- What is R-L-C series connection for A.C. circuit ? Explanation
- What is series combination of R-L circuit ? Explanation
- Define what is active power, reactive power, apparent power & power factor
- Explain what is series combination of R-C circuit in electrical engineering
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- relationship between line current & phase current for delta connected 3 load
- Relation between power consumed in a balanced star & delta connection

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