Parallel Resistor Equations

Parallel Resistor Calculator

Given n resistors in parallel (R₁, R₂, ..., R_n), the voltage across them remains the same whereas the current divides depending on the resistances. The equivalent resistance can be calculated as follows:

$$\Delta V = \left(I_1 + I_2 + ... +I_n \right) · R_{eq} \tag{1}$$

Since the current through each resistor is I_n = Δ V / R_n,

$$\Delta V = \Delta V · \left({1 \over R_1} + {1 \over R_2} + ... + {1 \over R_n} \right) · R_{eq} \tag{2} $$

Then, the equivalent resistance of the parallel is given by:

$$R_{eq} = \left( {1 \over R_1} + {1 \over R_2} + ... + {1 \over R_n} \right)^{-1} \tag{3} $$

If n=2, Eq (3) becomes:

$$R_{eq} = { {R_1 · R_2} \over {R_1 + R_2} } \tag{4} $$