## AC Series Circuit – Power, Electrical Resonance and Voltage Magnification

**AC Series Circuit:** The Circuit in which Voltage and Current varies both in Magnitude and Direction with time are called AC Circuits. The current in an Inductive Circuit (R-L Series circuit) Lags the Voltage by an angle Φ, which is called power factor angle. The current in the Capacitive Circuit (R-C Series circuit) Leads the Voltage by an angle Φ, which is also called power factor angle.

**Power and Power Factor:** There are three forms of power, 1) Active Power: P = V I CosΦ (Watt), 2) Apparent Power: P = V I (VA), and 3) Reactive Power: P = V I SinΦ. Power factor is equal to the ratio of Active Power to Apparent Power. The average power is also called as active power taken by the circuit and is measured in watts.

**Electrical Resonance:** An effect which is extremely important in Radio network. Under the condition of Resonance, the Voltage across the inductor and capacitor are equal and may be many times greater than the applied voltage. The Current is Maximum at resonance and such a series resonant circuit is often referred to as an acceptor circuit. The Quality Factor at resonant frequency fr is Q = 2*π*fr*L/R

**Voltage Magnification:** At resonant frequency fr, the voltage across L and C are equal and each is greater than the applied voltage. Hence, a voltage magnification occurs at the resonant condition. For a series resonant circuit the factor Q is measure of the voltage magnification. Therefore, Voltage Magnification is equal to Q Factor and Bandwidth of a series resonant circuit = ( f2 – f1 ) = R/(2*π*L)

**Reference:** V N Mittle and Arvind Mittal, “Basic Electrical Engineering”, Tata McGraw-Hill Education Private Limited, 2009.

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