Series: same current, voltages add
Resistors in series form one path, so the same current flows through each. Their voltages add up to the source voltage, and the larger resistor takes the larger share. The equivalent resistance is the sum, always more than the largest.
R_eq = R1 + R2 I = V / R_eq V1 = I·R1, V2 = I·R2
Parallel: same voltage, currents add
Resistors in parallel each sit across the source, so each sees the full voltage. Their currents add up to the total, and the smaller resistor takes the larger share. The equivalent resistance is always less than the smallest.
1/R_eq = 1/R1 + 1/R2 two resistors: R_eq = R1·R2 / (R1 + R2) I1 = V/R1, I2 = V/R2
Which resistor gets hot?
In series the larger resistor dissipates more (P = I²R, same I). In parallel the smaller one does (P = V²/R, same V). The power bars in the simulator flip when you switch topology.
Worked example (the simulator’s default values)
- V = 9 V, R1 = 220 Ω, R2 = 470 Ω.
- Series: R_eq = 690 Ω, I = 13.0 mA, V1 = 2.87 V, V2 = 6.13 V.
- Parallel: R_eq = 220·470/690 = 149.9 Ω, I = 60.1 mA, I1 = 40.9 mA, I2 = 19.1 mA.
Common mistakes
- Adding parallel resistances like series ones. Add conductances (1/R), not resistances.
- Expecting the parallel combination to be between the two values. It is always below the smallest.
- Assuming the bigger resistor always takes more power: true in series, false in parallel.
Common questions
How do you calculate resistors in parallel?
Add the reciprocals: 1/R_eq = 1/R1 + 1/R2 + … For two resistors, R_eq = R1·R2/(R1 + R2). 220 Ω and 470 Ω in parallel make 149.9 Ω.
What is the same in series and in parallel?
Series resistors carry the same current; parallel resistors have the same voltage across them.