Revision: 12th Std >> AC Circuits MAH-MHT CET (PCM/PCB) AC Circuits

The current driven by alternating voltage in a circuit is called alternating current.

The maximum value of an alternating current or voltage in either direction is called the peak value.

Voltage that varies with time periodically is called alternating voltage.

An a.c. generator is a device which converts the mechanical energy into the electrical energy using the principle of electromagnetic induction.

70.7% of the peak value of an alternating current or voltage (= 0.707 × peak value) is called the root mean square value or RMS value.

A graphical representation of the voltage and current in an alternating current circuit is called a phasor diagram.

A rotating vector that represents a quantity varying sinusoidally with time is called a phasor.

The opposing nature of inductor to the flow of alternating current is called inductive reactance.

Χ_L = `omega_"L" = 2 pi " f L"`

The effective resistance offered by an inductor to the alternating current is called inductive reactance.

The effective resistance offered by the capacitor is called capacitive reactance (ΧC).

`Χ_C = 1/omega_C`

`= 1/(2 pi fC)`

The effective resistance offered by a capacitor to the alternating current is called capacitive reactance.

The effective opposition offered by the inductor, capacitor and resistor connected in series to flow of AC current. is called impedance.

Z = `sqrt("R"^2 + (Χ_"L" - Χ_"C")^2)`

The Power Factor is the ratio of True Power (measured in Watts) to Apparent Power (measured in Volt-Amperes) in an AC circuit.

Power factor (cos Φ) = `"True power"/"Apparent power"`

In the expression Pav = V_rmsI_rms cos⁡ ϕ, the quantity cos φ is called the power factor.

The current flowing in a purely inductive or purely capacitive circuit for which cos φ = 0 and no power is dissipated even though the current is flowing is called wattless current.

When a charged capacitor is allowed to discharge through a non-resistive inductor, electrical oscillations of constant amplitude and frequency are produced; these are called L-C oscillations.

The condition in an L-C-R circuit in which current is maximum or impedance is minimum (or vice-versa) in an AC circuit, when ωL = 1/ωC and voltage is in phase with the current, is called resonance.

A device having high inductance and negligible resistance, used in AC circuits for adjusting current to any required value such that power loss in the circuit can be minimised (based on the principle of wattless current), is called a choke coil.

RMS value = 0.707 × peak value

Average value of alternating current or emf = 0.637 × peak value

X_L ​= 2πfL (∝ f)

X_C​ = \[\frac {1}{2πfC}\]​ (∝ 1/f)

Z = \[\sqrt{R^2+(X_L-X_C)^2}\] = \[\sqrt{R^2+\left(\omega L-\frac{1}{\omega C}\right)^2}\]

e = e₀​sin ωt

ϕ = tan⁻¹\[\left(\frac{X_C-X_L}{R}\right)\]

P_av ​= VI cos ϕ = I²Z cos ϕ = \[\frac {V_m​I_m}{2}\]​​cos ϕ = V_rms​I_rms​ cos ϕ

P = VI = \[\frac{V_mI_m}{2}[\cos\phi-\cos(2\omega t+\phi)]\]

 f = \[\frac {1}{2π\sqrt {LC}}\]

Q = \[\frac {1}{R}\]\[\sqrt {\frac {​L}{C}}\]​​