Parallel circuits

​​In a nutshell

In parallel circuits, the components are placed on different branches which run parallel to one another. The current gets split across the branches and the potential difference of each branch is the same. As there are multiple pathways for current to take, if one component breaks then the rest of the circuit can still work. The total resistance of the circuit is less than the branch with the smallest resistance.  

Current in a parallel circuit

Current flows from the power supply, around the circuit and back to the power supply. In a parallel circuit, the current will have more than one pathway to take around the circuit. 

When the current gets to a branch, some of the current will flow down one pathway and some will flow down another. Assuming that the resistance of each branch is the same, the current will get split equally across both branches. If the branches have different resistances then the more current will flow down the branch with least resistance. 

​Charge has to be conserved, which means that current doesn't get used up around the circuit.

As current is the flow of charge, the charge flowing into a branch must be the same as the current flowing out of the branch. Current flowing into the first branch is $$I_1$$, current flowing out of the branch is $$I_2$$ and $$I_3$$. After the current flows through the resistors, it joins together again to make $$I_4$$.

Mathematically, $$I_1=I_2+I_3=I_4$$

Potential difference in a parallel circuit

When the electrons leave the power supply, they are given some electrical energy to transfer around the circuit. When the current splits at branches, the electrons will travel down different paths, but will have the same electrical energy they had from the power supply. 

This means that the current gets split down the multiple pathways, the electrons are still carrying same energy they had from the power supply. Therefore the potential difference along each pathway is the same as the power supply, because the electrons haven't used any energy yet.

As the current leaves the battery, it moves around the circuit and arrives at point X. 

At point X, the current splits between the two pathways. Assuming the two resistors are equal, the current would be split equally along each path.

The electrons still contain the electrical energy from the power supply as they haven't travelled through any components yet.

Therefore when the electrons travel down one path, they still have the same amount of potential difference as the power supply.

Resistance in a parallel circuit

Now current has more than one path, the current will take the path of least resistance at branches. This means that more current will flow along the path with the smallest total resistance. 

As there is more current flowing down the path of least resistance, the total resistance of the whole circuit will be less than the branch with the smallest resistance. 

In the diagram, there are two resistors in parallel. There is a $$200 \, \Omega$$ resistor and a $$50 \, \Omega$$ resistor.

More current will flow down the $$50 \, \Omega$$ branch as more current will take the path of least resistance. ​

Ohm's law can be used to show this, $$V=IR \rightarrow I=\frac VR$$​​ The potential difference along each branch is the same as the power supply, as explained above.

The total resistance would be less than the resistance of the smallest branch. So the total resistance of this circuit would be $$R_T<50\,\Omega$$.​​​