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A series circuit is where components (e.g. resistors) are connected send to end to form a complete loop with a power source (e.g. a battery).
By considering electric current is a flow of electrons in a conductor, it could be easily visualized that the number of electrons passing through each component remain unchanged, as these electrons pass each component in turn and there is no other way that the electrons could go. Therefore, the current flowing in each component in a series circuit is the same.
Voltage is the release of elctrical energy per unit charge. Physically, it can be considered as the energy given out by each electron when it passes through a component. Since the same electron would pass through each component in turn in a series circuit, the sum of energy released by this single electron gives an indicating of the total voltage applied to the circuit (in fact, the total energy released by all electrons gives numerically the voltage of the power source).
The flow of electrons in a series circuit is affected by the resistances of its components. A higher resistance of a component leads to less number of electrons that could pass the component in a second. This means that the current in the circuit is reduced.
When comparing the energy released in a high resistant component with a low resistant one, an electron needs more energy (from the battery) to overcome the high resistance of a component than when it passes through a low resistance one in order to maintain a constant flowing of electrons in each component. In other words, the voltage across a high resistance component is higher than that across a low resistance one.