# Series Circuits

Series circuits are circuits with multiples resistors connected together on a single path like the image below. In this image, we have only two resistors but you could have a lot more of resistors in series. In series circuit, the current flowing through the resistors is the same for all resistors but the voltage is divided among the resistors. Example : In the image above, we have 12V from the D.C voltage source but the voltage is going to be split between the two resistors (V1 for the voltage across R1 and V2 for the voltage across R2). V1 + V2 is going to be equal to 12V in this case. There is multiple way we could calculated the voltage of each resistor. We will calculate V1 and V2 voltage using Ohm’s Law but you could use the equation for the voltage divider also.

We can calculate the voltage across both resistor by first calculating the current flowing through the circuit. Once we have the current flowing into the circuit, we can use Ohm’s law to calculate the voltage of each resistor. But we have a problem, we can’t calculate the current when we have two resistors. We need to find an equivalent circuit with only one resistor so we can use Ohm’s law. In a series circuit, you only need to add R1 and R2 to get you equivalent circuit. We can now calculate the current flowing in the circuit. We will use Ohm’s law for this. $I=\cfrac{V}{R}=\cfrac{12V}{Req}=\cfrac{12V}{R1+R2}$

If R1 = 100 ohms and R2 = 50 ohms, the current would be equal to: $I=\cfrac{12V}{100\Omega+50\Omega}=\cfrac{12V}{150\Omega}=0.08A=80mA$

We can now calculate the voltage across both resistors using Ohm’s law: $V=R*I$ $V1=R1*I=100\Omega*0.08A=8V$ $V2=R2*I=50\Omega*0.08A=4V$