Electrical circuits

An electric circuit is defined as a closed path for charge to flow between two points in an electrical system.

The three basic components of an electric circuit consist of:
- Power Supply: This component maintains a difference in electric potential between two points in the circuit, providing the necessary energy.
- Conductors: These are materials, typically wires, that allow the flow of electric current. They form the pathways for the charge to travel.
- Loads: Any device that utilizes electrical energy, such as light bulbs, resistors, etc.

A circuit diagram is a representation of how the components of an electric circuit are interconnected.
The different components are represented by unique symbols, which are standardized across the field of electrical engineering.

Positive Terminal: Represented by the longer line in a diagram.
Power Source (ΔV or Voltmeter V): Indicates the source of voltage in the circuit.
Light Bulb: Symbolizes a load that converts electrical energy into light.
Junction: A point in the circuit where two or more conductors meet.
Switch: Used to open or close the circuit.
Ammeter: Measures the current flowing in the circuit.
Conducting Wire: Typically shown as straight lines connecting components.
Resistor: Limits the flow of current in the circuit.

Conventional Current: Defined as the flow of positive charge. It moves from the positive terminal to the negative terminal of the power source.
Electron Flow: In reality, electrons flow from the negative terminal to the positive terminal, which is opposite to the conventional current flow.
It is essential to distinguish between these two flows for accurate analysis of circuits.

Developed by Gustav Kirchhoff in 1845, these laws govern how current and voltage operate in electrical circuits:
- Kirchhoff's First Law: States that the total current entering a junction must equal the total current leaving the junction.
  - This can be represented mathematically as:
    I1 = I2 + I3 where $I1$ is the incoming current and $I2$, $I3$ are the outgoing currents.
- Kirchhoff's Second Law: States that in any closed loop in a circuit, the sum of the potential differences (voltage) must equal zero.
  - This can be expressed as:
    riangle V = riangle V1 + riangle V2 + riangle V_3 where $ riangle V$ is the total voltage around the loop.
The implication is that all voltage supplied by the power source(s) is consumed by the components in the loop.

For Kirchhoff’s First Law:
- Given currents: $I1 = 0.5 A$, $I2 = 0.3 A$.
- Find $I3$: I3 = I1 - I2 = 0.5 A - 0.3 A = 0.2 A
For Kirchhoff's Second Law:
- Given potential differences:
  - Total voltage, $ riangle V = 12 V$
  - Load voltages: $ riangle V1 = 7 V$, $ riangle V2 = 3 V$.
- Find $ riangle V2$: riangle V2 = riangle V - ( riangle V1 + riangle V3)
  riangle V_2 = 12 V - (7 V + 3 V) = 2 V

Definition: Two components are in series when the charge flows through both components in a single path.
Current: The current remains the same for all components in series:
I = I1 = I2 = I_3
Total Resistance: The total resistance in a circuit with components in series is the sum of the individual resistances:
Rt = R1 + R2 + R3

Given resistances:
- $R_1 = 4 ext{ Ω}$
- $R_2 = 8 ext{ Ω}$
- $R_3 = 12 ext{ Ω}$
Total resistance calculation:
R_t = 4Ω + 8Ω + 12Ω = 24Ω
Further calculations determine the current:
- Given voltage, $ riangle V = 12 V$, find the current:
  I = rac{ riangle V}{R_t} = rac{12V}{24Ω} = 0.5A

Definition: Parallel components are connected along multiple pathways, allowing current to divide.
Potential Difference: The potential difference (voltage) is the same across all components in parallel:
riangle V = riangle V1 = riangle V2

The total resistance for components in parallel is calculated as the sum of the reciprocals of the individual resistances:
rac{1}{Rt} = rac{1}{R1} + rac{1}{R2} + rac{1}{R3}

Given resistances in parallel:
- $R_1 = 58 ext{ Ω}$
- $R_2 = 70 ext{ Ω}$
- $R_3 = 42 ext{ Ω}$
The calculation for total resistance:
rac{1}{R_t} = rac{1}{58} + rac{1}{70} + rac{1}{42}

Understanding the principles of circuit analysis, including the behavior of components in both series and parallel configurations, is vital for analyzing and designing electrical circuits effectively.
Kirchhoff's Laws are foundational concepts that assist in predicting circuit behavior analytically, helping to manage various electrical applications seamlessly.