created at May 31, 2021 (changed at August 26, 2021)

Equivalent resistance

Equivalent resistance Re is resistance of a single conductor (resistor), which could replace the initial set of resistors, giving the same effect.

Resistors can be connected either serially, or in parallel (or mixed). For serial connection the equivalent resistance is a sum of all connected resistances:

R_{s} = R_{1} + R_{2} + ... + R_{n}

For parallel connection, equivalent resistance can be obtained from:

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + ... + \frac{1}{R_{n}}

When resistors are connected serially, the same current flows through all of them. The voltage dropping on each resistor is proportional on its resistance, and can be computed as R·I.

For parallel connection, the same voltage is applied to all resistors, the separate electric current is flowing in each resistor branch: I = U/R. The total current flowing through a set of parallel resistors is a sum of all branch currents.