Understanding Electrical Dipoles and Circuit Connections

Current in Series

Because there is only one path, the intensity of the current ($I$) is identical at every point in a series circuit. If you have three resistors in a row, the current flowing through the first is exactly the same as the current flowing through the last.

Voltage in Series

While the current remains constant, the total voltage supplied by the source is distributed among the various dipoles. The sum of the individual voltages across each component equals the total voltage of the circuit. Mathematically, for $n$ dipoles in series:

$$U_{total} = U_{1} + U_{2} + \dots + U_{n}$$

Exam Tip: If one component in a series circuit fails (like a bulb burning out), the circuit is broken, and the current stops flowing entirely. This is why old Christmas tree lights used to go dark all at once if one bulb broke.

Parallel Connections: Multiple Branches

In a parallel connection, the terminals of the dipoles are connected to the same two points. This creates multiple "branches" or paths for the electricity to travel through.

Voltage in Parallel

The defining characteristic of a parallel circuit is that the voltage across each branch is identical. Because every branch is connected directly to the same two nodes of the power source, the potential difference remains constant for every component.

$$U_{total} = U_{1} = U_{2} = \dots = U_{n}$$

Current in Parallel (Derivation)

While the voltage is the same, the total current provided by the source is split among the different branches. According to the principle of conservation of charge, the total current entering a junction must equal the sum of the currents leaving it. Therefore, the total current ($I_{total}$) is the sum of the currents in each individual branch:

$$I_{total} = I_{1} + I_{2} + \dots + I_{n}$$

Summary Comparison Table

To help consolidate your understanding, refer to the following comparison between the two types of connections:

By understanding these fundamental rules of dipoles and connections, you can begin to predict how energy will be distributed in any electrical system, from a simple flashlight to the complex wiring of a modern home.