Parallel Circuits

What is a Parallel Circuit?

A parallel circuit is an electrical circuit configuration where the components are connected in such a way that there are multiple pathways for the electric current to flow. In a parallel circuit, each component has its own separate branch connected directly across the power source (usually a voltage source, such as a battery or power supply).

In a parallel circuit:

Parallel circuits are commonly used in electrical systems to power multiple devices simultaneously while maintaining consistent voltage across each device. They are also used in homes and buildings for lighting circuits and power outlets, where different electrical loads can operate independently.

Rules of a Parallel Circuit

A parallel circuit is defined as having multiple paths through which current can flow. From this definition, there are three rules for parallel circuits  as follows: 

*If components share two common nodes, they are in parallel.

All legs have the same and equal starting voltage.

Branch currents add up to total current. 

Individual Resistances diminish to the total resistance.

Adding Resistance in parallel

Adding resistance in parallel is less straightforward than adding resistors in parallel. According to the rules of Parallel circuits above, individual resistances diminish to total resistance. This is because there are multiple paths for current to flow and resistance is dissipated over multiple pathways. All this said, the equation which you can probably deduce on your own is as follows:

According to Ohm’s law, the currents flowing through the individual resistors are I1=V/R1, I2 = V/R2, and I3=V/R3. Conservation of charge implies that the total current is the sum of these currents: 

 It= I1+I2+13     →     It= V/R1 + V/R2 + V/R3     →     It= V(1/R1 + 1/R2 + 1/R3)

From here, we can create our formula for adding resistance in parallel if we isolate our units further. Our final formula for adding resistance in parallel is as shown below:


In this example, we have three resistors. This means we can shorten the equation above to be Rt = 1/(1/R1 + 1/R2+ 1/R3.)

Rt = 1/(1/1000 + 1/10000+ 1/100000)

Rt = 1/(.001 + .0001+ .00001)

Rt = 1/.00111

Rt = 900.09

Adding Resistance Tips

When adding only two resistors, you can divide the product by the sum.

If you have multiple resistors of the same value in parallel, the total resistance is the value of them divided by the number of them. 

The total resistance in parallel is always less than the lowest value of a resistor in the circuit.

Adding Capacitance in Parallel

Understanding how to add Capacitance in series takes a little more thought and understanding. If you need a deeper understanding of capacitors, see the MakerLessons' page on Capacitors. By placing any capacitors in series, we are effectively spacing the plates of a Capacitor at the start and end further from each other. If you think of this now as just one extra-wide capacitor, it makes sense that more distance between plates will decrease total capacitance. So, in the equation below, you will see that the total capacitance for capacitors in series will always add up to less than the smallest addend. 


In this example, we have three resistors. This means we can shorten the equation above to be Ct = C1 + C2.

C1= 10uF (.00001)                                C2 = 1uF (.000001)

Ct = .00001 + .000001

Ct = .000011 or 11uF

Voltage Drops

We do not consider Voltage drops in a truly parallel circuit because if all the legs of the circuit share the same two nodes of the power source, the voltage drop will be the entire voltage over each leg. That said, if any leg of a parallel circuit has more than one component in it, then we are talking about a combination series/parallel circuit where there will still be conventional voltage drops. See our page Combination Circuits for details. 

Adding Parallel current

Since each branch of the circuit has its own current flow, it makes sense that the total current for the circuit would be the addition of all of the branch's currents combined. In this example, with three parallel branches, the formula for total current would be: I = I1 + I2 + I3. Let's break that down a little. 

Using Ohm's Law we can find the current over each leg:

I = V/R1 = 9/1000 = .009  I = V/R1 = 9/10000 = .0009  

 I = V/R1 = 9/10000 = .00009

Once we have all the individual currents over each branch, we can simply add them to find total current. This will come out as follows:

I = I1 + I2 + I3 = .009 + .0009 + .00009 = .00999A or 9.99 mA


For exercises and projects that explore Series Circuits, see our Electronics Projects Page. The first set of activities are Resistors in a Circuit which expand on the concepts of Parallel Circuits like adding resistance, parallel current flow, and power over components.