Bioinstrumentation - Introduction to Biomedical Engineering - page 526

or rewritten in terms of an equivalent resistance R EQ as

R EQ ¼ V s

I ¼ R

þ R þ R

1 2 3

In general, if we have N resistors in series,

N

R EQ ¼

1 R i

ð 9 : 13 Þ

i ¼

Resistors in Parallel
Two or more elements are said to be in parallel if the same voltage is across each of the
resistors. Consider the three parallel resistors shown in Figure 9.17. We use a shorthand
notation to represent resistors in parallel using the k symbol. Thus, in Figure 9.17,

R EQ ¼ R k R k R : An equivalent circuit for Figure 9.17 is derived through KCL as

1 2 3

I þ V s
R

1 þ V s 2 þ V s 3 ¼

0

R R

or rewritten in terms of an equivalent resistance R EQ as

R EQ ¼ V s

1

I ¼

1
R 1 þ

1
R 2 þ

1
R 3

In general, if we have N resistors in parallel,

1

R EQ ¼ ð 9 : 14 Þ

1
R

1
R

1
R N

1 þ 2 þþ

For just two resistors in parallel, Eq. (9.14) is written as

R R

1 2

R EQ ¼ R k R ¼ ð 9 : 15 Þ

1 2

R þ R

1 2

I

+
−

V S R 1 R 2 R 3

FIGURE 9.17 A parallel circuit.