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Question
Explain the equivalent resistance of a series resistor network.
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Solution
When two or more resistors are connected end to end, they are said to be in series. The resistors could be simple resistors or bulbs or heating elements or other devices. Fig. (a) shows three resistors R1, R2 and R3 connected in series.
Three resistors in series
The amount of charge passing through resistor R1 must also pass through resistors R2 and R3 since the charges cannot accumulate anywhere in the circuit. Due to this reason, the current I passing through all the three resistors is the same. According to Ohm’s law, if same current pass through different resistors of different values, then the potential difference across each resistor must be different. Let V1, V2 and V3 be the potential difference (voltage) across each of the resistors R1, R2 and R3 respectively, then we can write V1 = IR1, V2 = IR2 and V3= IR3. But the total voltage V is equal to the sum of voltages across each resistor.
V = V1 + V2 + V3
= IR1 + IR2 + IR3 ….. (1)
V = I(R1 + R2 +R3)
V = I.RS …… (2)
where Rs = R1 + R2 R3 ……. (3)
When several resistances are connected in series, the total or equivalent resistance is the sum of the individual resistances as shown in the following figure.
Equivalent resistance (RS) has the same current
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