Resistors in Parallel

When resistors are connected so that each one provides a separate path for current, they’re in parallel. Parallel circuits behave very differently from series circuits, and the MCAT tests these differences relentlessly.

The defining feature of parallel: there are multiple paths current can take. Each resistor has its own branch.

The Parallel Rules

Picture the water park installing three slides side-by-side, all starting at the same upper pool and ending at the same lower pool. Each slide is a separate path. Water splits up among the three slides — but every slide starts and ends at the same elevation. That’s a parallel circuit.

The voltage is the same across every resistor in parallel.

This makes intuitive sense: adding another slide (even a narrow one) gives water more paths, so total flow goes up and total opposition goes down.

Current Division

Since every resistor has the same voltage across it, Ohm’s law tells you that more current flows through smaller resistors:

• $I_1 = V/R_1$, $I_2 = V/R_2$, $I_3 = V/R_3$.
• Total current: $I_{total} = I_1 + I_2 + I_3 + \ldots$.

The Product-Over-Sum Shortcut

For exactly two resistors in parallel, there’s a much faster formula than the reciprocal one:

This only works for two resistors. For three or more, you need the reciprocal formula (or pair them up two at a time).

N Equal Resistors in Parallel

When $N$ identical resistors (each $R$) are in parallel, the formula simplifies beautifully:

Parallel Circuit Summary

Series vs. Parallel: The One Table to Remember

If you internalize this contrast, series-and-parallel problems become almost mechanical.