Series circuits

Formula for equivalent resistance

When several resistors are connected in series, their combined effect on the circuit can be expressed as a single equivalent resistance. This equivalent resistance is obtained by simply adding together the values of all the connected resistors:

R_eq = R₁ + R₂ + R₃ +…+ R_n

The current that flows through each resistor is the same, and the total voltage applied to the circuit is divided among them. In this way, the equivalent resistance represents the total opposition to the flow of current in that single path formed by the series resistors.

Practical example

Let’s suppose we have three resistors connected in series with values of 10 Ω, 20 Ω, and 30 Ω. The equivalent resistance of the circuit is found by directly adding their values:

R_eq = 10 + 20 + 30 = 60 Ω

This means that, from the perspective of the power source, the set of resistors behaves like a single 60 Ω resistor. The current flowing through each resistor is the same, while the total applied voltage is shared among them in proportion to their resistance value. For example, if the source provides 12 V, the voltage drop will be 2 V across the 10 Ω resistor, 4 V across the 20 Ω resistor, and 6 V across the 30 Ω resistor, which adds up to the total 12 V.