CIRCUIT & FIELD THEORY
Group A


Circuit Theory
Graph of a network. Concept of tree, loop current and node pair voltage. Tie set and tie set
matrices-cut set and cut set matrices. Solution of equilibrium equations on loop and node
basis. Application of Laplace transforms for solving transient equations of electrical circuits.
initial and final value theorems. Unit step, impulse and ramp inputs. Laplace transform for
shifted and singular functions. The. convolution integral. Fourier series and its applications.
Exponential form of the Fourier series. Relation between frequency spectra and. Laplace
transform of the Fourier series. The concept of complex frequency, transform impedance and
admittance; series and parallel. combinations.

Network theorems: Thevenin, Norton, Reciprocity, Superposition and Telegen. Terminals
and ports. Driving point and transfer impedances. S-plane representation: Poles and zeros.
Time domain behaviour from pole and zero plots. Procedure for finding network functions
for general two-port network. Radian frequency and sinusoidal network functions in terms of
poles and zeros. Resonance, Q-factor and bandwidth. Asymptotic change of magnitude with
frequency in terms of poles and zeros. The symmetrical lattice..

Group B


Field Theory
Vectors and vector calculus. Gradient, divergence and curl of a vector. Gauss, Stokes and
Helmholtz theorems.
Electrostatics: Potential and electric field intensity. Conducting boundaries, Coaxial spheres
and cylinders. Laplace's and Poisson's equations. Electrostatic energy. Uniqueness theorem.
Method of images; dipoles. Dielectric polarisation, electric flux density, permittivity.
Boundary conditions. Stationary currents. Ohm's law; E.M.F. conservation of charge.
Resistance of arbitrary shaped conductors. Boundary conditions and refraction, current flow lines. Numerical solutions of Laplace's equation by the method of iterations.
Magneto static : Magnetic field intensity and flux density. Vector potential. Magnetic
dipole. Divergence of B. Ampere's law of force. Ampere's circuital law. Differential equation for vector potential. Magnetic polarisation and permeability. Boundary conditions for and H.
Time varying fields: Faraday's law. Dynamically and statically induced E.M.F's. Inductance
and stored energy. Hysteresis loss, Maxwell's equations. Displacement current. Deviation of generalised wave equations from v1axwell's equations for the magnetic vector potential.
specialization to Eddy current or diffusion equations and non dissipative wave equations.
Plane wave propagation and eddy current phenomenon as solutions of the above relevant
equations. Reflection and refraction of plane waves at the plane boundary of electromagnetic media.

 

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