Series & Parallel R – Equivalent Resistance Practice
Rₜ = R₁ + R₂ — Parallel: Rₜ = R₁R₂/(R₁+R₂)
Series resistors add: Rₜ = R₁ + R₂. Two in parallel use Rₜ = R₁R₂/(R₁+R₂), always less than the smaller R.
Guide — how to use this formula
- 1. Identify series (add) vs parallel (product/sum).
- 2. Convert kΩ → Ω when asked for ohms.
- 3. After Rₜ, use I = V/Rₜ.
- 4. Parallel Rₜ < each individual R.
Derivation
From Kirchhoff rules for two resistors:
- Series (same current):
R_t = R_1 + R_2 - Parallel (same voltage):
R_t = \frac{R_1 R_2}{R_1 + R_2}
Equal parallel pair → Rₜ = R/2.
Examples
Example: series 2+4
Rₜ = 6 Ω.
Example: parallel 3∥6
Rₜ = 2 Ω.