82 CIRCUIT ANALYSIS TECHNIQUES

`EXAMPLE 2.3.1`

Determine the voltage across the 20-resistor in the following circuit of Figure E2.3.1 (a) with

the application of superposition.

`(a)`

`V`

3

`6 Ω`

`6 A`

18 V V 12 Ω 80 Ω 20 Ω

`+`

`−`

`+`

`−`

`Figure E2.3.1`

`(b)`

`V′`

`A B`

`3`

`VA′`

3

`6 Ω`

`18 V VA′^ =^ V′ 12 Ω = 80 Ω 20 Ω`

`+`

`−`

`+`

`−`

`I 1 ′`

`(c)`

`V′′`

`A B`

`3`

`VA′′`

3

`6 Ω`

`VA′′ = V′′^12 Ω =^80 Ω^20 Ω`

`+`

`−`

`6 A`

`Solution`

`Let us suppress the independent sources in turn, recognizing that there are two independent`

sources. First, by replacing the independent current source with an open circuit, the circuit is

drawn in Figure E2.3.1(b). Notice the designation ofV′across the 12-resistor andV′/3 as the

dependent current source for this case. At nodeB,

(

1

80

`+`

`1`

20

`)`

VB′=

`VA′`

3

`or VB′=`

`VA′`

48

`For the mesh on the left-hand side,( 6 + 12 )I 1 ′=18, orI 1 ′=1 A. But,I 1 ′=VA′/12, orVA′ =12 V.`

The voltage across the 20-resistor from this part of the solution is

`VB′=`

`12`

48

`=`

`1`

4

`V`