4.2 Resistors in Series and Parallel

Series resistors

In a series circuit, resistors share the same current since there's only one path for charge to flow. The equivalent resistance is the sum: R_eq = R1 + R2 + ... The voltage across each resistor differs, dividing proportionally to resistance (V = IR for each).

Parallel resistors

In a parallel circuit, resistors share the same voltage across each branch. The equivalent resistance follows 1/R_eq = 1/R1 + 1/R2 + ..., which is always less than the smallest individual resistor. Current divides among branches inversely proportional to resistance.

Combining circuits

Complex circuits can be simplified by identifying groups of resistors in series or parallel and reducing them step-by-step into a single equivalent resistance. Applying Kirchhoff's laws (loop and junction rules) confirms current and voltage relationships in these combined networks.

Key terms

Series resistor formula

R_eq = R1 + R2 + R3 + ... (current same, voltage divides)

Parallel resistor formula

1/R_eq = 1/R1 + 1/R2 + ... (voltage same, current divides)

Current in series circuits

Same through every resistor since there's only one path for charge flow.

Voltage in parallel circuits

Same across every branch since branches connect the same two nodes.

Equivalent resistance in parallel

Always smaller than the smallest individual resistor because more current paths reduce total resistance.

Try an AP-style question

What is the equivalent resistance of 4 Ω and 12 Ω in parallel?

1. 8 Ω
2. 16 Ω
3. 48 Ω
4. 3 Ω