Electrical year 1 semester 1

Basic Concepts

• Electric charge underlies all electrical phenomena; charge separation creates electric fields, and charge movement constitutes electric current.
• Symbol Q denotes charge, measured in Coulombs (C).

Charge

• Exists in discrete units as multiples of electron charge.
  • Electron charge: -1.6 × 10^-19 C
  • Proton charge: +1.6 × 10^-19 C

Electric Current

• Symbol I represents the movement of charge (electrons) in Ampere or Amp (A).
  • 1mA (milli-amp) = 0.001 A
  • 1μA (micro-amp) = 10^-6 A
  • 1kA (kilo-amp) = 1000 A
• 1 Ampère is defined as the flow of 1 Coulomb of charge per second.

Charge, Current, and Time

• Relationship: Q = I × t, where Q is charge (C), I is current (A), and t is time (s).
• Current is the rate of charge flow: I = Q/t.

Potential Difference

• It arises from separated positive and negative charges, resulting in an electric field.
• It is measured in Volts (V), typically relative to a 0V reference (earth or ground).

Electrical System Analogy

• Voltage (potential difference) is analogous to water pressure.
• Electric current is analogous to water flow.

Energy and Power

• Energy is needed to separate charge, leading to potential difference.
• Equation: E = V × Q, where E is energy (Joules, J), V is voltage (Volts, V), and Q is charge (Coulombs, C).
• Power is the rate of doing work: P = E/t = V × I (Watts).

Resistance

• It is opposition to charge flow due to collisions within a material, converting electrical energy to heat.
• It is the material property that impedes the flow of charge
• Represented by the symbol R
• Unit: Ohm (Ω).
• Resistors are energy sinks, converting electrical to thermal energy.

Ohm's Law

• It defines the relationship between current (I), voltage (V), and resistance (R): V = I × R.
• Alternative forms: I = V/R, R = V/I
• When using formulas such as P=I^2R use the correct voltage, or it will cause mistakes
• To find the total power, P_T, use the total voltage or total resistance, (R1 + R2):

Material Classification by Resistance

• Conductors allow free charge flow.
• Insulators prevent charge flow.
• Semiconductors have controllable conductivity between conductor and insulator.

Conductor Properties

• The ability of a conductor to pass current depends on dimensions and material.
• Resistance formula: R = ρL/A, where ρ is resistivity (Ohm-metres), L is length, and A is cross-sectional area.
• Conductivity (σ) is the reciprocal of resistivity: σ = 1/ρ, measured in Siemens per metre (S/m).

Temperature Effects on Resistance

• Metal resistance increases with temperature; carbon and insulators decrease.
• Temperature coefficient of resistance (α) is the change in resistance per °C, relative to resistance at 0°C.

Connecting Resistances in Series

• The same current flows through each resistor.
• Total resistance: RT = R1 + R2 + R3 + ... + RN
• Source voltage is dropped across all resistors: Vs = V1 + V2.

Connecting Resistances in Parallel

• The total current, I, splits into distinct pathways
• Voltage is the same across each resistor.
• Total resistance: 1/RT = 1/R1 + 1/R2 + 1/R3 + ... + 1/RN

Quick Calculation for Two Resistors in Parallel

• Equivalent resistance: RP = (R1 × R2) / (R1 + R2).
• Current division: I1 = IT × [R2 / (R1 + R2)], I2 = IT × [R1 / (R1 + R2)]

Non-Ideal Voltage Sources

• Real cells/batteries have internal resistance.
• Terminal voltage varies with drawn current and causes power dissipation.
• Formula VT = VS - IR; where VR is the terminal voltage, VS is the unloaded supply voltage, I is the current and R is the internal resistance.

Maximum Power Transfer

• Occurs when load resistance equals source's internal resistance (resistance matching).
• Efficiency is only 50% under these conditions.

Battery Specifications

• Capacity is often measured in Ampere-hours (A-h).

Efficiency

• Defined as (P_OUTPUT / P_INPUT) × 100%.
• Efficiency decreases if load is too small compared to the internal resistance.

Current Sources

• Ideal current sources provide a constant current.
• Practical sources have internal resistance in parallel.

Network Analysis

• Involves solving electrical networks using methods like Superposition, Kirchhoff's Laws, Thévenin, and Norton circuits.
• Only considers circuits with resistors and d.c. sources
• More complex circuits can use these methods if they contain inductance, capacitance or fed from a.c. or d.c. sources.
• A network is a number of branches or circuit elements connected together and considered as a unit.
• If the network has no source of e.m.f. it is termed a PASSIVE network
• If the network has source of e.m.f. it is termed an ACTIVE network

Superposition Theorem

• The effect of an emf is the same whether it acts alone or with other emfs only in linear networks.
• Analyze each emf source separately, representing others by internal resistances.
• Resultant currents are algebraic sums from each source.

Kirchhoff's Laws

• It's necessary to define the meaning of Nodes, Loops and Branches before this is done

Kirchhoff's 1st Law

• (Current Law): The algebraic sum of instantaneous currents entering a node is zero.
• Σ i = 0 at any node.

Kirchhoff's 2nd Law

• (Voltage Law): The algebraic sum of instantaneous voltages around a loop is zero.
• Σ v = 0 for any closed loop.
• Direction of currents is arbitrary, resistors are energy sinks, sources are increases in potential from negative to positive. Choose the direction of the current and the draw the voltages in the oppositive direction to the current

Thevenin's Theorem

• Networks with 2 terminals (A and B) can be replaced by a constant voltage source.
• If circuits often change load resistance
• A magnitude which is equal to open circuit voltage between A and B, and internal resistance, r
• Saves analyzing the full network when different loads are connected
• r is the resistance between A and B with the load disconnected and emf sources replaced by there internal resistance.

Norton's Theorem

• Norton builds upon Thevenin
• Active network with 2 terminals (A and B) are replaced by constant current source, Is
• Is is equal to the short circuit at the terminals and a shunt resistance r, which is equal to the resistance betweeen (A and B) with the sources removed.

Explore the impact of internal resistance on voltage sources and how it affects terminal voltage when current is drawn. Investigate circuit analysis techniques, including node analysis and mesh analysis, and understand the principles of superposition in circuits with multiple voltage sources. Learn about battery discharge and circuit components.