Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

example: 3.1-6
(i) Find the currents in all the resistors in the circuit in Fig. 3.1-15. (ii) Find the voltage appearing 
across the current source and the power delivered by it.
10 A
0.1 S
0.05 S
0.03 S
0.02 S
Fig. 3.1-15 
Circuit for Example 3.1-6 
Solution
(i) Total current in a parallel combination gets distributed in resistors as per the conductance ratio. 
The relevant ratio here is 0.1:0.05:0.03:0.02, i.e., 10:5:3:2. Therefore, the currents are 5 A, 2.5 A, 
1.5 A and 1 A in 0.1 S, 0.05 S, 0.03 S and 0.02 S resistors, respectively.
(ii) The equivalent conductance of a parallel combination is the sum of conductance values of the 
participating resistors. Hence, the equivalent conductance here is 0.2 S. Therefore equivalent 
resistance is 5 
W
. Therefore, the voltage appearing across the current source is 50 V and the power 
delivered by it is 500 W.
3.2 
the Inductor
The physical basis for the two-terminal element called inductor has been dealt with in Chapter 1. Its 
unit will be V-s/A or Wb-T/A, which is given the name ‘Henry’ and abbreviated as ‘H’. The element 
relation for inductor as per passive sign convention is 
www.TechnicalBooksPDF.com

---

3.10
Single Element Circuits
i
+
–
v
L
y
y
( )
( )
( )
( )
t
L i t
t
L
v t
=
=
where
instantaneous flux linkage in 
==
=
=
−∞
−∞
∫
∫
L
di t
dt
i t
L
v t dt
t
v t dt
t
t
( )
( )
( )
( )
( )
;
and
1
y
We have emphasised the time-varying nature of variables by including (t) in the defining equations. 
However, we will use the italicised variables without the (t) attached to them also to stand for 
functions of time. Thus i and i(t) mean the same. We use the latter only when we want to emphasise 
the dependence on time.
We take up a detailed study of the element relation of an inductor.
The voltage across inductor is proportional to the rate of change of current through it. 
The current through the inductor is proportional to the area under the voltage waveform, 
i.e
., the V-sec product (or Wb-T) applied across its terminals from 
t
=
-∞
where 
t
=
-∞
has to be understood as the moment this inductor came into being.
These two simple statements have many implications in circuits in which inductors appear, which 
are described in the subsequent sub–sections.