0195136047.pdf

42 CIRCUIT CONCEPTS

EXAMPLE 1.3.2

For the circuit shown in Figure E1.3.2, use KCL and KVL to determinei 1 ,i 2 ,vbdandvx. Also,

findveb.

d

e

a b f c

+

−

+

−

+

+−

−

+ −

8 A

20 V

3 V

i 1 =?

ab = 5 V ibf

i 2 =?

−3 A

10 A 8 V

υ

υbd =?

+

−

υx =?

Figure E1.3.2

Solution

Using KCL at nodec,weget

i 1 = 8 +(− 3 =5A

Using KCL at nodef, we have

ibf=i 1 −(− 3 )= 5 + 3 =8A

Applying KCL at nodeb,weget

10 =i 2 +ibf=i 2 +8ori 2 =2A

Using KVL around the loopabdeain the clockwise direction, we have

vab+vbd+vde+vea= 0

or

5 +vbd+ 8 − 20 =0orvbd= 20 − 8 − 5 =7V

Note that in writing KVL equations with+and−polarity symbols, we write the voltage with a

positive sign if the+is encountered before the−and with a negative sign if the−is encountered

first as we move around the loop.

Applying KVL around the loopabfceain the clockwise direction, we get

vab+vbf+vfc+vce+vea= 0

or

5 + 0 + 3 +vx+(− 20 )=0orvx= 20 − 3 − 5 =12 V

Note that a direct connection betweenbandfimplies ideal connection, and hence no voltage

between these points.

The student is encouraged to rewrite the loop equations by traversing the closed path in the

anticlockwise direction.

Noting thatveb=ved+vdb, we have