Copyright 20 13 Dorling Kindersley (India) Pvt. Ltd

 
 
1.33
A circuit can get coupled to the surroundings by electrostatic/electromagnetic coupling with 
other physically separate circuits in the vicinity or by mechanical, thermal or optical interaction 
with the environment. Consider an isolated circuit that has no energy coupling of any kind with the 
surroundings. Obviously, the total energy in that circuit has to remain constant in time. That is, the 
sum of energy delivered to all the elements in the circuit must remain constant. Let there be n two-
terminal elements connected in such a circuit. Some of them may be electrical sources. Then,
E t
E t
E t
n
1
2
( )
( )
( )
+
+ +
=
Constant
Differentiating this equation both sides with respect to time, we get,
dE t
dt
dE t
dt
dE t
dt
n
1
2
0
( )
( )
( )
+
+ +
=
But each term in this equation is nothing but the instantaneous power delivered to the corresponding 
two-terminal element. Therefore,
p t
i
Over all the
elements in an
isolated circuit
( )
=
∑
0
(1.6-2)
Thus, the sum of instantaneous power delivered to all elements in an isolated circuit is always 
zero. Or equivalently, the sum of instantaneous power delivered by all elements in an isolated circuit 
is always zero. This implies that total power delivered by the elements that deliver positive power at t 
must be equal to the total power absorbed by the elements that absorb positive power at that instant. 
This principle can be employed to check the solution of a circuit analysis problem.
Note that ‘power delivered to an element’ and ‘power absorbed by an element’ mean the same.
The instantaneous power delivered to a two-terminal element does not have to be positive at all 
instants of time. Neither does it have to be negative at all instants. It is always positive in the case of 
a resistance. But in all other cases, it can be positive or negative depending on the relative polarity of 
voltage and current in the element.