Lesson : Parallel Circuits – HyperElectronic

In the previous lessons, we’ve looked at series circuits with resistors. Series circuits acts differently than a parallel circuits and we will now look at how a parallel circuits behave. The parallel circuit is represent below. In this case, we have only two resistors but you could have a huge amount of resistors in parallel if you want. In a parallel circuit, the voltage across the resistors is the same for all resistors but the current is divide among the two resistors. The current is not necessarily divide equally as we will see later. In our case, the voltage for R1 and R2 is going to be 12V. The current is split between the two resistors (I₁ and I₂). The total current (I_tot) of the circuit will be equal to the sum of I₁ and I₂. Parallel circuit are easier to solve since we only have to apply Ohm’s law to all the resistors to find either the voltage, currents or resistances.

We will now solve the example above. For this example: R1 = 100 Ω and R2 = 150 Ω. The voltage source is 12V. We will calculate the current I₁, I₂ and I_tot. After that, we will calculate the equivalent circuit.

Using Ohm’s law, we can calculate both I₁ and I₂:

$I=\cfrac{V}{R}$

$I_{1}=\cfrac{12V}{100\Omega}=0.12A=120mA$

$I_{2}=\cfrac{12V}{150\Omega}=0.08A=80mA$

We can now calculate I_tot:

$I=I_{1}+I_{2}$

$I_{tot}=0.12A+0.08A=200mA$

Like series circuit, we can simplify the circuit to an equivalent circuit with only one resistor. For parallel circuit, it is rarely used to solve problem since it doesn’t give us a lot of information. It could be used to find the voltage if we only had the total current and the values of the resistors. This would allow us to find the voltage applied to both resistors then you will be able to calculate the current flowing into both resistors (I₁ and I₂).

Figure 2 : Equivalent circuit for a parallel circuit

The equation for the resistor Req of the equivalent circuit is :

$Req=\cfrac{1}{\cfrac{1}{R1}+\cfrac{1}{R2}}$

If we reuse the example above, we would have :

$Req=\cfrac{1}{\cfrac{1}{100\Omega}+\cfrac{1}{150\Omega}}=60\Omega$

To verify if we have the appropriate value for Req, we can calculate I_tot of the equivalent circuit and we should get the same value that we have calculated before.

$\cfrac{V}{R}=I_{tot}=\cfrac{12V}{60\Omega} = 0.2A = 200mA$

We obtained the same value as before so we know our equivalent circuit is correct. If we had more than two resistors, the generic formula to calculate Req would be:

$Req=\cfrac{1}{\cfrac{1}{R1}+\cfrac{1}{R2}+\cfrac{1}{Rn}+\dots}$

The next lesson will be dedicated to multiples examples of series and parallel circuit. We will review Ohm’s law and Power law at the same time.