Consider an ac circuit containing resistance of R ohms, inductance of L henries and capacitance of C farads connected in series, as shown in Fig. 4.23 (a).

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

ADVERTISEMENTS:

Voltage drop across inductance, V_{L}= IωL leading I by π/2 radians or 90°

Voltage drop across capacitance, V_{C} = I/ω C or IX_{C} lagging behind I by π/2 radians or 90°

V_{L} and V_{C} are 180″ 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_{L} or V_{C}) is predominant. Let us consider the case when V_{L} is greater than V_{C}.

**The applied voltage V, being equal to the phasor sum of V _{R}, V_{L} and V_{C} is given in magnitude by:**

**Phase angle ****ɸ**** between voltage and current is given by:**

ɸ will be + ve i.e. applied voltage will lead the current if X_{L} > X_{c} and 3> will be – ve i.e., applied 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 or V I cos ɸ.

**Reactance:**

Inductive reactance, X_{L} is directly proportional to frequency being equal to ωL or 2 π f L and capacitive reactance, X_{C} is inversely proportional to frequency being equal to 1/ω C or 1/2 π fC.

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 are connected in series, their effects neutralize each other and their combined effect is then their difference.

ADVERTISEMENTS:

**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: **

X = X_{L} – X_{C}

When X_{L} > X_{C} i.e. X_{L} – X_{C} is positive, the circuit is inductive and phase angle is ɸ positive.

When X_{L} < X_{C} i.e. X_{L} – X_{C} is negative, the circuit is capacitive and phase angle is ɸ negative.

ADVERTISEMENTS:

When X_{L} = X_{C} i.e. X_{L} – X_{C} = 0, the circuit is purely resistive and phase angle ɸ is zero.

**If the expression for applied voltage is taken as:**

v = V_{max} Sin^{ }ωt

**Then expression for the current will be:**

The value of ɸ will be positive when current leads i.e., when X_{C} > X_{L} and negative when current lags i.e., when X_{L} > X_{C}.