2 Resistors in parallel calculator
Calculator and formulas for calculating parallel circuits with two resistors
This specialized calculator enables the calculation of parallel circuits with exactly two resistors. You can either calculate the total resistance from two known individual resistors or determine an unknown parallel resistor R₂ when the total resistance and R₁ are known.
- Calculate total resistance: From R₁ and R₂ → Rtotal
- Calculate parallel resistor R₂: From R₁ and Rtotal → R₂
Functionality: In a parallel resistor circuit, the resistors are connected parallel to each other. The same voltage is applied across all resistors, but the current divides according to the resistance values.
Application: Select the desired calculation mode, enter the known values and click "Calculate". The calculator supports various unit prefixes (mΩ, Ω, kΩ, MΩ).
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Circuit diagram: Parallel connection of two resistors
Formulas for parallel circuits with two resistors
1. Calculate total resistance (product formula)
When both individual resistors R₁ and R₂ are known, the total resistance can be calculated using the product formula:
\[ R_{total} = \frac{R_1 \cdot R_2}{R_1 + R_2} \]
This formula is a simplification of the general parallel circuit formula for exactly two resistors.
2. Calculate parallel resistor R₂
When the total resistance Rtotal and resistor R₁ are known, the parallel resistor R₂ can be calculated by rearranging the product formula:
\[ R_2 = \frac{R_1 \cdot R_{total}}{R_1 - R_{total}} \]
Important: This formula is only valid when R₁ > Rtotal, since in parallel circuits the total resistance is always smaller than the smallest individual resistor.
3. Derivation via conductances
The product formula can also be derived via conductances (G = 1/R):
\[ G_{total} = G_1 + G_2 = \frac{1}{R_1} + \frac{1}{R_2} \]
Solving for Rtotal:
\[ R_{total} = \frac{1}{G_{total}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}} = \frac{R_1 \cdot R_2}{R_1 + R_2} \]
Practical calculation examples
Example 1: Calculate total resistance
Given: R₁ = 30Ω and R₂ = 20Ω connected in parallel
Find: Total resistance Rtotal
Calculation using the product formula:
\[ R_{total} = \frac{R_1 \cdot R_2}{R_1 + R_2} = \frac{30 \times 20}{30 + 20} = \frac{600}{50} = 12Ω \]
Result: The total resistance is 12Ω
Check: 12Ω < 20Ω (smallest individual resistor) ✓
Example 2: Calculate parallel resistor R₂
Given: R₁ = 100Ω, desired total resistance Rtotal = 30Ω
Find: Parallel resistor R₂
Calculation:
\[ R_2 = \frac{R_1 \times R_{total}}{R_1 - R_{total}} = \frac{100 \times 30}{100 - 30} = \frac{3000}{70} = 42.86Ω \]
Result: The required parallel resistor R₂ is approximately 43Ω
Check: 30Ω < 43Ω < 100Ω ✓
Example 3: Equal resistors
Special case: When both resistors are equal (R₁ = R₂ = R), the formula simplifies to:
\[ R_{total} = \frac{R \times R}{R + R} = \frac{R^2}{2R} = \frac{R}{2} \]
Example: Two 100Ω resistors in parallel → Rtotal = 50Ω
Rule: With two equal resistors in parallel, the resistance value is halved.
Current distribution and practical applications
Current distribution
In a parallel circuit, the total current divides inversely proportional to the resistance values:
\[ I_1 = I_{total} \times \frac{R_2}{R_1 + R_2} \] \[ I_2 = I_{total} \times \frac{R_1}{R_1 + R_2} \]
Rule: More current flows through the smaller resistor.
Practical applications
- Reduce resistance values: Parallel connection to reduce total resistance
- Shunt resistors: Current measurement through parallel resistors to measuring instruments
- Voltage divider loading: Calculate effects of load currents
- LED circuits: Dropping resistors for parallel LED strings
- Bias circuits: Operating point adjustment in amplifier circuits
- The total resistance is always smaller than the smallest individual resistor
- The total power increases with parallel connection (Ptotal = P₁ + P₂)
- Different resistance values result in different currents
- Pay attention to the power rating of individual resistors