Parallel circuit rules

The parallel circuit rules show how to use Ohm's law when the circuit has more than one device receiving electrical energy. It will also help us see how the resistance, the current, and the voltage change in the parallel circuit. A parallel circuit is shown below. Notice that the circuit has 2 switches (green), 1 voltage source of 24 volts, and 2 resistors. 

In a parallel circuit, the current has more than 1 pathway.

To be more precise, the circuit has 2 pathways or 2 branches.

Simply put, the current has the ability to "make choices" as to where it would go. If the current can either go this way or that way, then the circuit is a parallel circuit.

Look carefully at the circuit below and you will see that the current can either go to the 8 Ohms resistor or the 4 Ohms resistor. This is what we mean by "making choices."

Parallel circuit

Take a close look at the two red dots. Did you notice that both devices are connected to the same two red dots? This means that both devices are fed by the same voltage of 24 volts. 

Rule #1: Devices in parallel circuits have the same voltage as the voltage source.

Let V be the voltage feeding the circuit

Let V1 be the voltage feeding the device with the 4 Ohms resistor.

Let V2 be the voltage feeding the device with 8 Ohms resistor.

Then, V = V1 = V2

Now, let us talk about the current. Let us pretend that the resistance is the same in both branches.

Since there is a resistance, the current going there will be less.

Since the resistance is the same for both branches, it makes sense to say that both branches will receive the same amount of current.

Parallel circuit
The current I is split into I1 and I2. Half of the current will go to the branch with the 4 Ohms resistor and the other half to the branch with the 4 Ohms resistor.

If one resistor is equal to 4 Ohms and the other 8 Ohms like the first figure, more current will go to the branch with 4 Ohms. In fact twice as much current will go to the branch with a lesser resistance.

However, the amount of current that will go to the two branches must equal the amount that came from the source or the current I.

Rule #2: In parallel circuit, the current in the circuit is equal to the the sum of the currents in its parallel branches.

I = I1 + I2

Now we can find the resistance for the circuit using I = I1 + I2

Let R1 and R2 be the resistances in the 2 branches. Let Rp be the resistance of the circuit. The resistance of the circuit is usually called equivalent resistance. Ohm's law will apply separately to each branch.

I = I1 + I2

Rule #3:

1 / Rp
   =  
1 / R1
+  
1 / R2
1 / Rp
   =  
1 / R1
+  
1 / R2

Parallel circuit rules generalization

The parallel circuit rules can be summarized and generalized as below

Let V be the voltage feeding the circuit

Let V1, V2,..., Vn be the voltage feeding other devices in the branches

Then, V = V1 = V2 = ... = Vn

Let I be the current in the circuit

Let I1, I2,..., In be the current going to other devices in the branches

Then, I = I1 + I2 + ... + In

Let R1, R2, ... , Rn be the resistances in the branches. Let Rp be the equivalent resistance.

1 / Rp
   =  
1 / R1
+  
1 / R2
+ ...
+  
1 / Rn

Any questions about the parallel circuit rules? Send an email

Parallel circuits quiz

Take the parallel circuits quiz below to see how well you understand parallel circuits. After completing this quiz with 100% accuracy, you will know exactly how the current, the voltage, and the resistors behave in a parallel circuit. You will not need to use a paper and pencil to complete this quiz.

First, read the lesson about parallel circuits and then take this quiz.

Objective of the parallel circuit quiz:

  • Know how the current behaves in a parallel circuit
  • Know how the voltage behaves in a parallel circuit
  • Know how the resistor behaves in a parallel circuit
  • Know how to apply Ohm's law to find the current going through the circuit.
  • Find the current in the circuit
Test your knowledge with the quiz below:

1. The number of pathways the current can flow in a parallel circuit is equal to

equal to 0
equal to 1
greater than 1
usually greater than 2.

2. A parallel circuit usually has

1 device
more than 2 devices
no more more than 30 devices
at least 2 devices.

3. A parallel circuit has 2 branches. One branch has 1 resistor. The other branch has 1 lamp. The voltage in the circuit is 120 volts. The voltage in the lamps is

60 volts
120 volts
30 volts
Not enough information

4. A parallel circuit has 2 resistors with resistances 4 Ohms and 8 Ohms. The equivalent resistance will be

12 Ohms
smaller than 4 Ohms
6 Ohms
bigger than 6 Ohms

5. A parallel circuit has 6 branches. The resistance in one branch is increased by 6 Ohms. The current is that branch

will increase
will increase by 6 amperes
will decrease by 6 amperes
will decrease

6. A parallel circuit has 2 branches. Each branch has 1 resistor with the same resistance of 4 Ohms. The equivalent resistance is

4 Ohms
8 Ohms
2 Ohms
Not enough information

7. A parallel circuit with 2 branches is powered by a 20 volts battery. Each branch has 1 resistor with the same resistance of 2 Ohms. What is the current coming from the source?

20 amperes
10 amperes
5 amperes
15 amperes

8. In a parallel circuit, the current at the source is equal to the sum of all individual currents in the branches

Sometimes
Never
Not always
Always

9. A parallel circuit has 4 branches. Branch #1 has a 3 Ohms resistor. Branch #2 has a 5 Ohms resistor. Branch #3 has 2 Ohms resistor. Branch #4 has 6 Ohms resistor. Which branch will has a higher amperage?

Branch #1
Branch #2
Branch #3
Branch #4

10. A parallel circuit has 10 branches. Each branch has 1 resistor with the same resistance of R Ohms. The equivalent resistance is

10 + R
10*R
10/R
R/10



Score =

I strongly recommend you try your very best to complete this parallel circuits quiz on your own. Resist the urge to see the answers. Review the lesson about parallel circuit again. However, if you still cannot get 100% on your own, click here to see the answers.


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