Parallel Circuits

A 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 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 split between the resistors. The total current (Itot) of the circuit will be equal to the sum of all current (I1 and Ibelow) .

Like series circuit, we can simplify the circuit to an equivalent circuit with only one resistor. 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 apply to both resistors then you will be able to calculate the current flowing into both resistors (I1 and I2). Below you can find the equivalent circuit of the circuit we have above :

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

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

Example : R1 = 100 Ω and R2 = 150 Ω. The voltage source = 12V. We will calculate the current I1, I2 and Itot.

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

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

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

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

We can now calculate Itot :

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

$I=0.12A+0.08A=200mA$