0195136047.pdf

20 CIRCUIT CONCEPTS

(b) If such a 2-wire system is connected to a 110-V (rms) residential source outlet in order

to power a household appliance drawing a current of 1 A (rms), find the rms voltage at

the load terminals.

(c) Compute the power dissipated due to the extension cord.

(d) Repeat part (a) at 50°C, given that the temperature constant for copper is 241.5°C.

Solution

(a)d=64.1 mils= 64. 1 × 10 −^3 in= 64. 1 × 10 −^3 × 2 .54 cm/1in×1m/100 cm=

1. 628 × 10 −^3 m. From Table 1.2.1,ρof copper at 20°C is 17× 10 −^9 m,

l=100 ft=100 ft×

12 in

1ft

×

2 .54 cm

1in

×

1m

100 cm

= 30 .48 m

A=

πd^2

4

=

π( 1. 628 × 10 −^3 )^2

4

= 2. 08 × 10 −^6 m^2

Per Equation (1.2.2),

R20°C=

17 × 10 −^9 × 30. 48

2. 08 × 10 −^6

‘∼= 0. 25 

(b) Rms voltage at load terminals, V= 110 −( 0. 25 ) 2 = 109 .5 V (rms). Note that two

100-ft-long wires are needed for the power to be supplied.

(c) Power dissipated, per Equation (1.2.5),P=( 1 )^2 ( 0. 25 )( 2 )= 0 .5W.

(d) Per Equation (1.2.3),

ρ50°C=ρ20°C

(

50 + 241. 5

20 + 241. 5

)

=

17 × 10 −^9 × 291. 5

261. 5

= 18. 95 × 10 −^9 ·m

Hence,

R50°C=

18. 95 × 10 −^9 × 30. 48

2. 08 × 10 −^6

∼= 0. 28 

EXAMPLE 1.2.2

(a) Consider a series–parallel combination of resistors as shown in Figure E1.2.2(a). Find

the equivalent resistance as seen from terminalsA–B.

(b) Determine the currentIand powerPdelivered by a 10-V dc voltage source applied at

terminalsA–B, withAbeing at higher potential thanB.

(c) Replace the voltage source by an equivalent current source at terminalsA–B.

(d) Show the current and voltage distribution clearly in all branches of the original circuit

configuration.