Series circuit rules

The series circuit rules show how to apply Ohm's law when the circuit has more than one device receiving electrical energy.

It will also help us see how the current, the resistance, and the voltage change in the circuit. Here is an example of a series circuit. The circuit has 1 switch (green), 1 voltage source of 12 volts, and 3 resistors. 

Simply put, the current cannot "make choices" as to where it would go. If the current can either go this way or that way, then the circuit is not in series.

Look carefully at the circuit above and you will see that the current has to go through the path it is in. This fact leads us to Rule #1.

Let I be the current going through the circuit

Let I₁ be the current going through the 1 Ohm resistor.

Let I₂ be the current going through the device with 2 Ohms resistor.

Let I₃ be the current going through the 3 Ohms resistor.

Then, I = I₁ = I₂ = I₃

This series circuit has 3 resistors. Recall that a resistor is a device that resists the flow of current. Does it make sense to you that the current will be resisted by all 3 resistors? It will indeed!

For example, to find the total resistance for our circuit above, just add 1, 2, and 3.

Total resistance = 1 + 2 + 3 = 6 Ohms.

We can now use Ohm's law to find the intensity of the current flowing through the circuit.

I = 2 amperes

Whenever the current go through a device, a voltage drop or potential difference occurs because of the resistor in that device. It simply means that the voltage in that device will not be the same as the voltage source. 

Voltage_{across 1 Ohm resistor} = R × I = 1 × 2 = 2 volts

Voltage_{across device with 2 Ohms resistor} = R × I = 2 × 2 = 4 volts

Voltage_{across 3 Ohms resistor} = R × I = 3 × 2 = 6 volts

From this, there is an important observation we need to make.

Notice that 12 volts  = 2 + 4 + 6

Let V be the voltage at the source

Let v₁ be the voltage across the 1 Ohm resistor.

Let v₂ be the voltage across the device with 2 Ohms resistor.

Let v₃ be the voltage across the 3 Ohms resistor.

Then, V = v₁ + v₂ + v₃

Series circuit rules generalization

The series circuit rules can be summarized and generalized as follow:

Let I be the current going through the circuit

Let I₁, I₂,..., I_n be the current going through other devices.

Then, I = I₁ = I₂ = ... = I_n

Let R₁, R₂,..., R_n be the resistance of devices in the circuit.

Then, R = R₁ + R₂ + ... + R_n

Let V be the voltage at the source

Let v₁,v₂,...,v_n be the voltage drop across other devices.

Then, V = v₁ + v₂ +...+ v_n