Calculate Equivalent Resistance of Resistors in Parallel
Number of Resistors
R1 (Ω)
R2 (Ω)
Result
Equivalent Resistance
Reciprocal Sum
Step-by-Step Calculation
Parallel Resistance Formula
1/Rt = 1/R1 + 1/R2 + ... + 1/Rn
Rt = 1 / (1/R1 + 1/R2 + ... + 1/Rn)
For 2 resistors: Rt = (R1 × R2) / (R1 + R2)
Special case (n equal): Rt = R / n
In parallel, the equivalent resistance is always less than the smallest resistor. More resistors in parallel = lower total resistance = higher total current from the source.
⚠All resistor values must be positive and non-zero. The formula uses reciprocals, so zero resistance would cause division by zero.
What is Parallel Resistance?
Resistors in parallel share the same voltage across them but split the current. The total current is the sum of individual currents. The equivalent resistance decreases because more conductive paths are added. This is opposite to series where resistance adds.
Reciprocal Rule
Add reciprocals of each resistance, then take reciprocal of the sum. 1/Rt = Σ(1/Ri).
Two Resistor Shortcut
Product over sum: Rt = (R1×R2)/(R1+R2). Quick and useful for common 2-resistor parallel pairs.
Equal Resistors
n identical resistors of value R in parallel: Rt = R/n. Example: 4 × 100Ω = 25Ω.
Current Division
Current through each branch: Ii = It × (Rt/Ri). Smaller resistor = more current. Larger resistor = less current.
Teaching Example: R1=100Ω, R2=220Ω in parallel.
1/Rt = 1/100 + 1/220 = 0.01 + 0.004545 = 0.014545. Rt = 1/0.014545 ≈ 68.75Ω.
Verify: 68.75Ω is less than 100Ω (the smallest). Using product/sum: (100×220)/(100+220) = 22000/320 = 68.75Ω.
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