# CBSE Class 12th Physics Notes: Alternating Current (Part ‒ II)

Jan 6, 2017 16:00 IST

CBSE class 12 Physics chapter wise notes (or key notes) Part – 2 on chapter Alternating Current are available in this article. These key notes are important & very helpful for revision purpose before the CBSE board exam.

These key notes are continuation of CBSE Class 12th Physics Notes: Alternating Current (Part ‒ I). In part I, we have studied important concepts like Alternating Current, Alternating Voltage, Average Value of Alternating Current and Voltage, Root Mean Square value of Alternating Current, Phasors, Different Types of A.C. circuits, Charging and Discharging of a Capacitor etc. In this part (or Part 2) we will study the concepts given below:

 AC Voltage Applied to a Series LCR Circuit Resonance in a Series LCR Circuit Sharpness of Resonance: Quality Factor Power Dissipation in AC Circuit Power Factor Wattless Current LC Oscillations Analogies between LC oscillation of an (Electrical system) and Oscillation of a block at the end of a spring (Mechanical system)

The key notes are given below:

AC Voltage Applied to a Series LCR Circuit

For a series LCR circuit driven by voltage V = Vm sin ω t, the current is given by I = Im sin (ω tϕ). Here we make an assumption that XL > XC

Above relation is graphically shown in the figure given below

Here, e.m.f. is leading the current by phase angle ϕ and Z is called impedance of the circuit and is measure in ohm.

Note:

If XC > XL, ϕ is + ve and the circuit is predominantly capacitive. Consequently, the current in the circuit leads the source voltage.

If XC < XL, ϕ is ‒ ve and the circuit is predominantly inductive. Consequently, the current in the circuit lags the source voltage.

The root mean square voltage (Vrms) cannot be added arithmetically to the applied root mean square voltage, i.e., VrmsVL + VC + VR

Resonance in a Series LCR Circuit

A series RLC circuit exhibit the phenomenon of resonance. The circuit is said to be in resonance at a frequency fr called resonant frequency at which XL = XC.

Now,

f = fr current is maximum

f < fr & f > fr the current is less than its maximum value

A given series RLC circuit is

• Purely capacitive at a frequency, f < fr

• Purely inductive at a frequency, f > fr

• Purely resistive at a frequency, f = fr

During Resonance:

• The impedance of the circuit is minimum and is equal to R (i.e., Z = R).

• The root mean square value of current in the circuit is maximum and is equal to Vrms/R.

• The applied voltage and the current are in phase.

• The power dissipation in the circuit is maximum.

Sharpness of Resonance: Quality Factor

In a series RLC circuit, the quality factor (Q) measures sharpness of resonance.

Quality factor is given by, Q = (ωr L/R).

Power Dissipation in AC Circuit

The average power loss over a complete cycle is given by, Pav = Vrms Irms cos ϕ

In a series resonance circuit, ϕ = 0o therefore, Pav = Vrms Irms

ϕ is also equal to 0o for a purely resistive circuit.

For a purely inductive or a purely capacitive circuit, ϕ = 90o and Pav = 0.

Power Factor

The power factor, cos ϕ of an AC circuit is the ratio of true power dissipation to the apparent power dissipation in the circuit.

Also, cos ϕ = R / Z.

Range of power factor for an AC circuit lies between 0 and 1.

0 for purely inductive circuit.

1 for purely resistive circuit.

Wattless Current

If an electric circuit contains either inductance only or capacitance only, then the phase difference ϕ between current and voltage is 90o. The average power dissipated in such circuits is zero.

LC Oscillations

An inductor and a capacitor can store magnetic energy and electrical energy respectively.

If a capacitor (initially charged) is connected to an inductor then, the charge on the capacitor and the current in the circuit exhibit the phenomenon of electrical oscillations similar to oscillations in mechanical systems.

Analogies between LC oscillation of an (Electrical system) and Oscillation of a block at the end of a spring (Mechanical system)

 Electrical system Mechanical system Inductance L Mass, m Reciprocal capacitance 1/C Force constant, k Charge, q Displacement, x Curent, i = dq/dt Velocity, v = dx/dt Electromagnetic energy Mechanical energy U = ½ (q2/C) + ½ (L i2)] E = ½ (k x2 ) + ½ (m v2)]

CBSE Class 12th Physics Notes: Alternating Current (Part ‒ I)

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