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

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.

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

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

The mean value of alternating current is defined as the value of a steady (DC) current which would transfer the same amount of charge through a circuit in the same time as the alternating current does during one half cycle.

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.

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

Χ_L = `omega_"L" = 2 pi " f L"`

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

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

The square root of the mean of the squares of the instantaneous current values over one complete cycle, equal to i_m\[\sqrt{2}​\], is called the root mean square current (or effective current).

The voltage that varies sinusoidally with time, expressed as v = v_m sin⁡ ωt, is called alternating voltage.

The current whose magnitude changes with time and direction reverses periodically is called alternating current (AC).

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.

A series LCR circuit consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series to an AC voltage source.

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)`

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

OR

Power Factor is the cosine of the phase angle (φ) between the voltage and current in an AC circuit. It equals the ratio of true (average) power to apparent power.

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.

OR

Wattless Current (also called reactive current) is the component of current in a purely inductive or purely capacitive circuit that flows without consuming any power.

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"`

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.

\[I_{avg}=\frac{2}{\pi}I_0\]

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

RMS value = 0.707 × peak value

X_L ​= 2πfL (∝ f)

X_C​ = \[\frac {1}{2πfC}\]​ (∝ 1/f)

e = e₀​sin ωt

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

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

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

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

Where:

• V_m​ = Peak voltage
• I_m​ = Peak current
• ϕ = Phase angle between voltage and current
• ω = Angular frequency
• t = Time

\[\cos\phi=\frac{P_{av}}{P_{apparent}}=\frac{P_{av}}{V_{rms}\cdot I_{rms}}\]

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

 f = \[\frac {1}{2π\sqrt {LC}}\]