print this

Calculating Current in Series-Parallel Circuits

Figure 1. Series-parallel resistors.

In a circuit with resistors connected in both series and parallel, consider the circuit as a combination of parallel parts and series parts.

Use resistance formulas to determine the total resistances of the series and parallel parts. Then, use Ohm's Law to calculate the voltage drops across and currents through each part.

In the circuit of Figure 1, first use the parallel resistance formula to find the equivalent resistance R₁₂₃.

Then the series resistance formula tells us R_TOT = R₁₂₃ + R₄. So, Ohm's Law gives the total circuit current:

I_TOT equals both the current I₄ though R₄ and the current I₁₂₃ entering/exiting the parallel part. Using Ohm's Law:

So, knowing the value of V₁₂₃, again apply Ohm's Law to find the current I₁ through the parallel resistor R₁:

and similarly for I₂ and I₃.

An Example

Given the circuit in Figure 1, suppose E = 9 V, R₁ = 500 Ω, R₂ = 1.0 kΩ, R₃ = 1.5 kΩ, and R₄ = 220 Ω. Then R₁₂₃ = 273 Ω and R_TOT = 493 Ω, so

and thus

And similarly for I₂ and I₃.

Note: It is important to carefully handle units with metric prefixes. Above, we adjusted the decimal point and units so that our formula for current yielded volts/ohms = amperes.