Essential Concepts in Alternating Current and Wave Optics
Alternating Current (AC)
AC (L-7): The current which changes continuously with time and reverses its direction periodically is called AC. The instantaneous AC is given by I = I0 sin ωt.
DC: The current which is unidirectional (constant) is called DC.
RMS of AC over a complete cycle: It is defined as the square root of the mean of the square value of AC over a complete cycle. i.e., Irms = I0 / √2 = 0.707 I0.
Impedance: The combined opposition offered by reactance and resistance to the flow of alternating current is called impedance. It is denoted by Z.
Quality Factor (Q Factor): The sharpness of the resonance curve is measured by a factor called the quality factor or Q factor. Mathematically, it is defined as the ratio of inductive reactance to resistance.
Wattless Current: The current in an AC circuit is said to be wattless if the average power consumed in the circuit is zero. This happens in a pure inductive or capacitive circuit in which the voltage and current differ by a phase angle of π/2.
Transformer: An electrical device used to convert high voltage into low voltage and low voltage into high voltage. Two types:
- Step-up: Converts low voltage into high voltage (Np < Ns).
- Step-down: Converts high voltage into low voltage (Np > Ns).
Energy losses in transformer: Copper loss, iron loss, eddy current loss, flux leakage, and hysteresis loss.
AC Generator: An electrical device used to convert mechanical energy into electrical energy. Main parts: Field magnet, rectangular coil (armature), slip rings (R1 and R2), brushes (B1 and B2), and a source of energy.
Wave Optics
Reflection of light: The phenomenon of light bouncing back to the same medium after incident on a reflecting surface like a mirror.
Refraction of light: The phenomenon of the bending of a light ray as it passes from one medium to another.
Power of a lens: It is the reciprocal of the focal length of a lens. i.e., P = 1/f.
Critical Angle: The angle of incidence in the denser medium for which the angle of refraction in the rarer medium is 90°.
Wavefront: The continuous locus of all particles of the medium which are vibrating in the same phase at any instant. 3 types: Spherical wavefront, plane wavefront, and cylindrical wavefront.
Interference of light: When two light waves of the same frequency and having zero or constant phase difference superpose each other in the same direction, the intensity in the region of superposition gets redistributed, becoming maximum at some points and minimum at others. This phenomenon is called interference of light.
Fringe width: The distance between two consecutive bright fringes. β = λD / d.
Diffraction at a single slit:
- Central maximum: At the central point O, the secondary wavelets have zero path difference (they are in the same phase). They add up constructively to produce a central bright fringe.
- Calculation of path difference: The path difference between the wavelets from L and N is P = NP – LP = d sin θ.