Page 266 - Mechatronics with Experiments

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Notice that no current will pass through R since there is zero resistance path parallel to it,
2
therefore,
V s
i = (5.32)
1
R
1
Hence,
10 45
i = 5 A + A = A (5.33)
N
7 7
Referring to Figure 5.4c, the equivalent resistance in the dotted block as seen by the load is
again,
1 1 1
= + (5.34)
R eqv R 1 R 2
1 1
= + (5.35)
7 3
7 ⋅ 3
R eqv = = 2.1 Ω (5.36)
7 + 3
And it is confirmed that the relationship between Thevenin’s and Norton’s equivalent circuit,

V = R eqv ⋅ i N (5.37)
T
45
= 2.1 ⋅ = 13.5 V (5.38)
7

5.4 IMPEDANCE

5.4.1 Concept of Impedance

The term impedance is a generalization of the resistance. If a circuit consists of a potential
source and a resistor, the impedance and the resistance are the same thing. Impedance
is a generalized version of resistance when a circuit contains other components such as
capacitive and inductive components. The input–output relationship between voltage and
current in a resistor circuit is
V(t)
= R (5.39)
i(t)
Let us take the Fourier transform of this,
V(jw)
= R (5.40)
i(jw)
where in the frequency domain the input–output ratio is constant, R, not a function of
√
frequency, w, and j = −1. The impedance of a resistor is a real constant.
Let us examine an RL circuit (Figure 5.5a), and consider the input (current)–output
(voltage) relationship in the frequency domain. In Figures 5.5c and d, if the switch is
disconnected from the voltage supply lead (A) and connected to the other lead (B), that is
putting the voltage supply out of the circuit, the V(t) in the equations below would be set
to zero.
di(t)
V(t) = R ⋅ i(t) + L (5.41)
dt
V(jw)
= (R + jwL) (5.42)
i(jw)