Introduction to Ohm's Law, Sources of EMF, & Resistance - Electrical Course - Part 33

Ohm's Law, Electromotive Force (EMF), and Resistance are fundamental concepts in electrical engineering and physics. These concepts form the basis of how electrical circuits work, allowing for precise calculation and control of electrical parameters like voltage, current, and resistance. 1. Introduction to Ohm's Law Ohm's Law describes the relationship between voltage, current, and resistance in an electrical circuit. Discovered by the German physicist Georg Simon Ohm, this law is one of the most basic principles in electronics and electrical engineering. Ohm’s Law Formula: 𝑉 = 𝐼 × 𝑅 V=I×R where: 𝑉 V = Voltage (in volts, V) 𝐼 I = Current (in amperes, A) 𝑅 R = Resistance (in ohms, Ω) Explanation: Voltage ( 𝑉 V) is the electrical potential difference that drives current through a circuit. Current ( 𝐼 I) is the flow of electrons through a conductor. Resistance ( 𝑅 R) is the opposition to the flow of current. Applications: Determine Voltage: Given current and resistance, voltage can be calculated using 𝑉 = 𝐼 × 𝑅 V=I×R. Calculate Current: Given voltage and resistance, current can be calculated as 𝐼 = 𝑉 𝑅 I= R V ​ . Find Resistance: Given voltage and current, resistance can be calculated as 𝑅 = 𝑉 𝐼 R= I V ​ . Practical Example: If a circuit has a voltage of 12 volts and a resistance of 4 ohms, the current through the circuit is: 𝐼 = 𝑉 𝑅 = 12 4 = 3  amperes I= R V ​ = 4 12 ​ =3 amperes Ohm's Law helps electricians and engineers understand how changes in voltage or resistance affect the current in a circuit, which is essential for safe and effective circuit design. 2. Sources of Electromotive Force (EMF) Electromotive Force (EMF) is the energy provided per unit charge by an energy source, such as a battery or generator, to move electrons through a circuit. EMF is measured in volts (V) and represents the potential difference between the terminals of a source when no current flows. EMF vs. Voltage: EMF is the maximum potential difference a source can provide, while voltage (or terminal voltage) is the potential difference across the terminals of a source when it supplies current to a load. Voltage drops as current flows through the circuit due to internal resistance within the source, whereas EMF is the ideal, no-load voltage. Common Sources of EMF: Batteries: Convert chemical energy into electrical energy to provide a steady EMF for powering circuits. Generators: Convert mechanical energy into electrical energy, creating an EMF through electromagnetic induction (used in power plants and alternators). Solar Cells: Convert solar energy into electrical energy using photovoltaic (PV) cells, commonly used in solar panels. Thermocouples: Convert thermal energy into electrical energy, generating an EMF based on temperature differences, often used in temperature sensing and measurement. Formula for EMF in a Circuit with Internal Resistance: 𝑉 = EMF − ( 𝐼 × 𝑟 ) V=EMF−(I×r) where: 𝑉 V = Terminal voltage across the load EMF EMF = Electromotive force of the source 𝐼 I = Current flowing through the circuit 𝑟 r = Internal resistance of the source Example Calculation: If a battery has an EMF of 12V and an internal resistance of 0.5Ω, and it is supplying a current of 2A, the terminal voltage 𝑉 V is: 𝑉 = 12 − ( 2 × 0.5 ) = 12 − 1 = 11  volts V=12−(2×0.5)=12−1=11 volts 3. Understanding Resistance Resistance is the property of a material that opposes the flow of electric current, converting some of the electrical energy into heat. It is measured in ohms (Ω) and depends on the material, length, cross-sectional area, and temperature. Factors Affecting Resistance: Material: Conductors (e.g., copper, aluminum) have low resistance, while insulators (e.g., rubber, glass) have high resistance. Length: Longer conductors have higher resistance, as electrons encounter more obstacles. Cross-Sectional Area: Wider conductors have lower resistance because they provide more pathways for current. Temperature: For most conductors, resistance increases with temperature, while for some materials (like semiconductors), resistance may decrease as temperature rises. Formula for Resistance in a Uniform Conductor: 𝑅 = 𝜌 × 𝐿 𝐴 R=ρ× A L ​ where: 𝑅 R = Resistance (ohms, Ω) 𝜌 ρ = Resistivity of the material (ohm-meter, Ω·m) 𝐿 L = Length of the conductor (meters, m) 𝐴 A = Cross-sectional area of the conductor (square meters, m²) Example Calculation: Suppose a copper wire has a length of 10m and a cross-sectional area of 0.001   m 2 0.001m 2 . Given that copper has a resistivity of 1.68 × 1 0 − 8   Ω ⋅ 𝑚 1.68×10 −8 Ω⋅m, the resistance of the wire is: 𝑅 = 1.68 × 1 0 − 8 × 10 0.001 = 0.000168   Ω R=1.68×10 −8 × 0.001 10 ​ =0.000168Ω Resistance affects the efficiency of circuits, causing voltage drops and energy losses as heat, especially in longer runs or high-power applications.