Revision: Electromagnetic Induction and Alternating Currents >> Alternating Current Physics (Theory) ISC (Science) ISC Class 12 CISCE

A current whose magnitude varies continuously and whose direction reverses periodically.

Mathematically: I = I₀​ sin ωt

When a coil rotates in a magnetic field, it produces alternating voltage and current. These values reach their maximum in two positions of the coil. This maximum value is called the peak value or amplitude.

The time taken by the alternating current to complete one cycle is called the periodic time, denoted by T.

The number of cycles completed by an alternating current in one second is called the frequency of the current.

The RMS value of an alternating current is defined as the square root of the mean of the squares of the instantaneous current values, taken over one complete cycle.

The RMS value of AC is equal to that value of steady direct current (DC) which would produce the same amount of heat in a given resistor, over the same time, as the alternating current does over one complete cycle.

A phasor is a rotating vector that represents a sinusoidally varying quantity (like AC voltage or current). Its length represents the peak (maximum) value, and its angular position represents the instantaneous phase.

The angle by which one alternating quantity (current or voltage) leads or lags another of the same frequency.

A phasor diagram is a diagrammatic representation of two or more phasors of the same frequency, drawn to show their relative phase difference at a given instant.

A purely resistive AC circuit consists of a non-inductive resistor R connected directly across an alternating voltage source, with no inductor or capacitor present in the circuit.

The effective opposition offered by a capacitor to AC flow is given by X_C = \[\frac {1}{ωC}\] = \[\frac {1}{2πfC}\].

The reciprocal of reactance, 1/X_C​ is measured in siemens (S) or Ω⁻¹.

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.

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.

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.

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

An electrical device which converts low alternating voltage at high current to high alternating voltage at low current (or vice versa) — i.e., a device which reduces or increases the voltage in an AC circuit through mutual induction — is called a transformer.

The transformer is a device used for converting low voltage into high voltage and high voltage into low voltage. It works on the principle of electromagnetic induction.

T = \[\frac {2π}{ω​}\]

• f = \[\frac {1}{T}\]

Since T = \[\frac {2π}{ω}\]​: f = \[\frac {ω}{2π}\]

Unit: Cycles per second (c/s) or Hertz (Hz)

RMS Current = I_rms​ = \[\frac {I_0}{\sqrt 2}\]

Approx. Value - 0.707 I₀​

V_rms​ = \[\frac {V_0}{​\sqrt 2}\]

​Approx. Value - 0.707 V₀​

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

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

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

\[\frac{V_s}{V_p}=\frac{N_s}{N_p}=k\]

Where:

• V_s = Secondary (output) voltage (V)
• V_p = Primary (input) voltage (V)
• N_s = Number of turns in secondary coil
• N_p = Number of turns in primary coil
• k = Transformation ratio (turns ratio)

\[\frac{I_p}{I_s}=\frac{N_s}{N_p}=\frac{V_s}{V_p}\]

\[\frac{V_s}{V_p}=\frac{N_s}{N_p}=\frac{I_p}{I_s}=k\]

 P_input = P_output

A transformer is based on the principle of mutual induction, i.e., whenever the magnetic flux linked with a coil changes, an emf is induced in the neighbouring coil. For an ideal transformer there is no loss of power, so P_input = P_output​. On the basis of winding, transformers are of two types — step-up and step-down.