Q1. Answer all of the following :
(a)
Consider the following matrix A:
A = \beginbmatrix 0 & 1 \\ 0 & -2 \endbmatrix
Compute state transition matrix eAt.
(b)
Calculate the equivalent resistance R_{ab} in the circuit given below.
1Omega
1Omega
10 Omega
5Omega
3Omega
6Omega
12 Omega
4Omega
10 Omega
1Omega
5Omega
(c) Discuss in detail various factors affecting the resistivity of electrical materials.
(d) The electric field is given by E(r) = E0 cos((z)/(z0)) exp(-r/r0) \hatr, where z0 and r0 are constants. Check whether or not the electric field is conservative. If it is conservative find the potential, if it isn't suggest how it may be possible to find the electrostatic part of the electric field (if present) and the corresponding electrostatic potential V (r).
(e) Write a note on classification of analog instruments.