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Current & Resistance
7.7 Combination of Resistors
Some times the electric circuit consist of more than two resistors, which are,
connected either in parallel or in series the equivalent resistance is evaluated
as follow:
7.7.1 Resistors in Series:
The figure 7.4 shows three resistor in series, carrying a current I.
R 1
R 2
R 3
A B C D
V AB
V BC
V CD
V AD
Figure 7.4
For a series connection of resistors, the current is the same in each
resistor.
If V AD is the potential deference across the whole resistors, the electric
energy supplied to the system per second is IV AD . This is equal to the
electric energy dissipated per second in all the resistors.
Hence
IV AD = IV AB + IV BC + IV CD (7.17)
V AD = V AB + V BC + V CD (7.18)
The individual potential differences are
Therefore
V AB = IR 1 , V BC = IR 2 , V CD = IR 3
V AD = IR 1 + IR 2 + IR 3 (7.19)
V AD = I (R 1 + R 2 + R 3 ) (7.20)
The equivalent resistor is
R = R 1 + R 2 + R 3 (7.21)
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