28

CIRCUIT LAWS

3.6

[CHAP. 3

VOLTAGE DIVISION

A set of series-connected resistors as shown in Fig. 3-5 is referred to as a voltage divider. The concept extends beyond the set of resistors illustrated here and applies equally to impedances in series, as will be shown in Chapter 9.

Fig. 3-5

Since v1 ¼ iR1 and v ¼ iðR1 þ R2 þ R3 Þ,

 v1 ¼ v

R1 R1 þ R2 þ R3



EXAMPLE 3.7. A voltage divider circuit of two resistors is designed with a total resistance of the two resistors equal to 50.0 . If the output voltage is 10 percent of the input voltage, obtain the values of the two resistors in the circuit. v1 ¼ 0:10 v

0:10 ¼

R1 50:0  103

from which R1 ¼ 5:0 and R2 ¼ 45:0 .

3.7

CURRENT DIVISION

A parallel arrangement of resistors as shown in Fig. 3-6 results in a current divider. The ratio of the branch current i1 to the total current i illustrates the operation of the divider.

Fig. 3-6

v v v v þ þ and i1 ¼ R1 R2 R3 R1 i1 1=R1 R2 R3 ¼ ¼ i 1=R1 þ 1=R2 þ 1=R3 R1 R2 þ R1 R3 þ R2 R3 i¼

Then

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An