Series and Parallel Combination of Resistors

Redraw the circuit if needed. Identify resistors with the same current as series. Identify resistors connected between the same two nodes as parallel. Replace one simple group at a time by its equivalent resistance. Continue until a single resistance remains. Apply Ohm's law if source voltage is given.

Series diagram: resistors connected one after another in a single path. Parallel diagram: resistor branches connected between the same two junctions. Label current I in series and branch currents I_1, I_2 in parallel, with common voltage V across branches.

For 4 ohm and 12 ohm in parallel, writing R_p = 16 ohm is wrong because 16 ohm is the series sum, not the parallel equivalent.

A combination of resistors is an arrangement of two or more resistors connected in a circuit so that they can be replaced by a single equivalent resistance producing the same current-voltage effect between two terminals.

A combination of resistors is an arrangement of two or more resistors connected in a circuit so that they can be replaced by a single equivalent resistance producing the same current-voltage effect between two terminals. Series: R_s = R_1 + R_2 + R_3 + ..., same current through all resistors, voltage divides. Parallel: 1/R_p = 1/R_1 + 1/R_2 + 1/R_3 + ..., same voltage across each branch, current divides. SI unit of resistance is ohm. Use series formula only when components carry the same current; use parallel formula only when components share the same two terminals. Two resistors of 3 ohm and 6 ohm in series give 9 ohm. The same resistors in parallel give 2 ohm, which is smaller than both 3 ohm and 6 ohm.

In series, resistors are connected end to end and the same current passes through each resistor. The applied potential difference divides across them. In parallel, resistors are connected across the same two terminals, so the potential difference across each branch is the same and current divides among branches. Equivalent resistance is larger than any individual resistor in series and smaller than the smallest branch resistance in parallel. Series: R_s = R_1 + R_2 + R_3 + ..., same current through all resistors, voltage divides. Parallel: 1/R_p = 1/R_1 + 1/R_2 + 1/R_3 + ..., same voltage across each branch, current divides. SI unit of resistance is ohm. Use series formula only when components carry the same current; use parallel formula only when components share the same two terminals. Find equivalent resistance of 4 ohm and 12 ohm in parallel, then in series with 2 ohm. Parallel part: 1/R_p = 1/4 + 1/12 = 3/12 + 1/12 = 4/12 = 1/3, so R_p = 3 ohm. Total series resistance = 3 + 2 = 5 ohm. If connected to 10 V, current = 10/5 = 2 A. Questions may ask for equivalent resistance of mixed circuits, comparison of brightness of bulbs, current division, voltage division, or identifying series-parallel parts from a circuit diagram. For 4 ohm and 12 ohm in parallel, writing R_p = 16 ohm is wrong because 16 ohm is the series sum, not the parallel equivalent.