Electric Circuits: Conserving Charge and Energy within Circuits

Conservation of Charge

Charge conservation is grounded on the fundamental principle that electric charge cannot be created or destroyed within a closed system.
In an electric circuit, the total charge flowing into a junction is always equal to the total charge flowing out. This is referred to as Kirchhoff’s first law or the junction rule.
Suppose the sum of currents entering a junction is I1 + I2 + …, and the currents leaving the junction are Ia + Ib + …. Kirchhoff’s first law can be stated as: I1 + I2 + … = Ia + Ib + …

The principle of energy conservation states that the total energy in a closed system remains constant. Energy can neither be created nor destroyed, only transferred or converted to different forms.
In electrical circuits, the energy supplied by the source (like a battery or a generator) transfers energy to components (like resistors or lamps) where it’s converted to other forms (like heat or light).
Kirchhoff’s second law, also known as the loop or mesh rule, is a reflection of energy conservation in electric circuits. It states that the sum of the emf around any closed loop is equal to the sum of potential differences in that loop.
If we denote emfs as E1 + E2 + …, and potential differences as V1 + V2 + …, Kirchhoff’s second law is written as: E1 + E2 + … = V1 + V2 + …
In simpler terms, what this means is that the energy provided by the source is equal to the energy dissipated in the circuit’s resistive components.

Electrical power is the rate of energy conversion in a circuit, calculated as the product of current and voltage: P = IV.
Power can also be computed using the square of current times resistance (P = I²R) or the square of voltage over resistance (P = V²/R), depending on which values are known.
Units of power are Watts (W), where one watt equals one joule per second.

Comprehending these key concepts about charge and energy conservation is crucial when dealing with electric circuits. Good luck with your revision!