You can think of all electrical circuits, regardless of size, as collections of smaller series and parallel circuits. A series circuit arranges its components one after the other, as in a daisy chain, sharing voltage and current, according to well-defined rules. Other rules apply to combining devices such as resistor and capacitors in series: some are simple to work with, others have more complex behaviors.
An electrical circuit is a complete loop in which current from a power source flows through a set of components and back to the source's ground connection. In a series circuit, the current passes through one component at a time, one after the other. Each component in the series circuit has a pair of wires, called leads. One lead carries current into the device, and the other lead sends current to the next device.
The components in a series circuit share the power source’s voltage. The voltage across each device is a fraction of the total. If you add up the voltages across each component, you get the total voltage. Though components have a voltage across them, the voltage across a wire is always zero. In a direct current, or DC, circuit, one side of the component has a positive voltage, the other side becomes negative. You can measure the voltage across each device with a voltmeter.
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All the devices in a series circuit carry the same current. To find this current, divide the total voltage by the total of all ohm resistances in the circuit. For example, a circuit has two components of 10 ohms each, and a total voltage of 5 volts. Dividing 5 volts by a total of 20 ohms gives a current of .25 amps.
As current in a series circuit passes from one component to the next, and if any device fails, it interrupts the current to all devices. Likewise, if the connections between devices fail, the whole circuit fails. This fact makes it easy to turn a series circuit on and off; you need only one switch in the circuit, and can place it at any point in the circuit. However, it can make troubleshooting a large series circuit difficult, as any component or combination of components can cause a circuit failure.
Resistors, Capacitors and Inductors
The ohm value of resistors adds up in a series circuit. If you have a 1,000-ohm, a 500-ohm and a 68-ohm resistor in series, the total resistance is simply 1,568 ohms. Inductors add up the same way: three 100-henry inductors in series add up to a total inductance of 300 henrys. Capacitors, however, add up in a more complicated way. To find total capacitance of capacitors in series, divide 1 by each value, add them, and then take divided 1 by the result. For example, for a 10-microfarad and a 20-microfarad capacitor in series, add 1/10 to 1/20 and get .15. Divide 1 by .15 to obtain a total of 6.67 microfarads, a smaller value than either capacitor by itself.