PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

116 Practical MATLAB® Applications for Engineers

and

____di(t)
(dt)

= 0

since i(t) is a constant, then vL(t) = 0 V.

R.2.64 In a DC circuit, the steady-state current* through a capacitor (C) is always zero (A)
since

it C

dv t

C dt

()
C()

and

dv t

dt

C()
0

since vC(t) is a constant, then iC(t) = 0 A.

R.2.65 Note that R.2.63 and R.2.64 imply that in a DC circuit during the steady-state
response, that is, for t ≥ 5 τ,† a pure inductor and a pure capacitor can be replaced
by a short and an open circuit, respectively.

R.2.66 The effi ciency of a system denoted by η is defi ned as the ratio of the output power
divided by its input power. Then

 = (PO/PI) * 100%

where PO denotes the output power and PI its input power, both in watts.

R.2.67 Mesh or loop analysis (fi rst proposed by Maxwell) refers to a procedure in which,
given an electrical network that consists for simplicity of resistors and voltage
sources can be expressed as a set of equations in terms of its loop currents by apply-
ing KVL around each of the independent loops of the network. The resulting set of
equations is suffi cient to determine all the network currents.

R.2.68 The steps involved in obtaining the set of loop equations are

a. Assign a clockwise direction to each of the loop currents of the n loops of an

electrical network, and label the unknown loop currents I 1 , I 2 , I 3 , I 4 , ..., In.

b. For each one of the independent n loops, write the corresponding loop equation

by applying KVL around the loop.

c. A set of n equations in terms of the n unknown currents are then obtained.

d. Solve the set of n equations for the n unknown currents (I 1 , I 2 , I 3 , I 4 , ..., In).

e. A branch of the electrical network, which is a part of two adjacent loops, labeled

x and y, with loop currents Ix and Iy respectively, results in a net branch current

that is the algebraic sum of the two currents Ix and Iy (Ix − Iy) where 1 < x ≤ n and

1 < y ≤ n.

*^ The concept of steady state is introduced later on in this chapter. At this point, consider steady state as the
stable or fi nal current.
† τ is referred to as the time constant of the circuit introduced and discussed later on in this chapter. For simple
fi rst-order circuits, τ is either RC or L/R.