A series circuit has only one path for the current to flow. An example of a series circuit can be seen in figure 1 below. To complete the circuit, the current must flow from the negative terminal of the battery through resistor R1 and then through resistor R2 before returning to the positive terminal of the battery. Note that the same amount of current passes through both R1 and R2. There is nowhere else for the current to go. This is the key concept of a series circuit. The current flow is the same through each component of the circuit.
In a series circuit, to find the total resistance of all components, you simply add the individual resistances together. In the case of figure 1, R1 is 5 ohms and R2 is 10 ohms. That makes a total of 15 ohms for the circuit. This total is usually written as Rtotal or Requiv Knowing the voltage (30 volts) and resistance (15 Ω) of the circuit, you can now calculate the current using Ohm's Law:
I = V/R Simply plug in 30 volts for V and 15 ohms for R and you get
I = 30v/15Ω = 2 amperes.
Knowing the current that is flowing through the circuit and knowing that it is constant allows you to use Ohm's Law to determine how much voltage is being applied across each resistor. In the case of R1, the resistance is 5 ohms and the current is 2 amperes. Using Ohm's Law to solve for voltage,
V = IR becomes
V = 2 amperes × 5 ohms = 10 volts.
Next solve for the voltage across R2,
V = 2 amperes × 10 ohms = 20 volts. Notice that the voltage drop across R1 (10 volts) and the voltage drop across R2 (20 volts) add up to 30 volts which is the total voltage of the battery. That is not a coincidence but is another key concept of series circuits. The sum of the voltage drops across all components will equal the source voltage of the circuit.