Page 116 - MATLAB an introduction with applications

Electrical Circuits ——— 101

i R 1 R 2 R 3
A B
V 1 V 2 V 3
V
Fig. 2.7 Series circuit

V = V 1 + V 2 + V 3
where V 1 = iR 1
V 2 = iR 2
and V 3 = iR 3
V
Hence = R 1 + R 2 + R 3
i
Therefore, the combined resistance R of the series circuit is given by

R = R 1 + R 2 + R 3
Parallel Circuits: For the parallel electrical circuit shown in Fig. 2.8, we can write
V
i 1 =
R 1
V
i 2 =
R 2
V
and i 3 =
R 3
i
i 3
i 1
i 2
V R 1 R 2 R 3

Fig. 2.8 Parallel circuit
Now i = i 1 + i 2 + i 3
Therefore,
V V V V
i = + + =
R 1 R 2 R 3 R
where R is the combined resistance. Hence
1 = 1 + 1 + 1
R R 1 R 2 R 3

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