Question

Explain the equivalent resistance of a series resistor network.

Answer 1

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 = IR_1, 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.R_S …… (2)
where R_s = 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 (R_S) has the same current