Revision: Class 12 >> Alternating Current NEET (UG) Alternating Current

It is the rate of flow of charge which changes the magnitude and direction periodically, as a result of which voltage also varies in the same manner along with current.

The alternating voltage or current is expressed in terms of peak (maximum) value, average (mean) value or effective (rms) value.

The average value of AC current shows an equal amount of charges in DC current,

\[V_{avg}=\frac{2}{\pi}V_{peak}\]

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 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.

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

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.

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.

RMS value = 0.707 × peak value

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

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

\[Z=\sqrt{R^2+(X_L-X_C)^2}\]

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

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

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

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

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.

Inductive Reactance (XL)

• X_L= ωL = 2πfL
•  Increases with frequency
•  Voltage leads current

Capacitive Reactance (XC)

• \[X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}\]
• Decreases with frequency
• Current leads voltage

• Series circuit with R, L, C
• The same current flows through all components
• Net Reactance: \[X=X_L-X_C=\omega L-\frac{1}{\omega C}\]
• Impedance (Z): \[Z=\sqrt{R^2+(X_L-X_C)^2}\]
• Phase Angle: \[\tan\phi=\frac{X_L-X_C}{R}\]
• Power Factor: \[\cos\phi=\frac{R}{Z}\]

Resonance occurs when a single Lewis structure cannot adequately represent the actual structure of a molecule — multiple valid Lewis structures (called canonical forms) can be drawn.

• The actual molecule does not switch between these structures; it is a resonance hybrid — a weighted average of all canonical forms.

• The energy of the resonance hybrid is always lower than the energy of any single canonical form (this energy difference is called resonance energy or resonance stabilisation energy).

• All canonical forms must have: the same positions of atoms, the same number of paired and unpaired electrons, and similar energy.

Classic examples:

• CO₃²⁻ (carbonate ion): 3 equivalent resonance structures — each C − O bond is neither single nor double, but intermediate (~1.33 bond order)
• Ozone (O₃): 2 resonance structures with bond length ~128 pm (intermediate between O − O single bond ~148 pm and O = O double bond ~121 pm)