Understanding Electrical Energy, Power, and Resistance

Electrical Resistance and Ohm's Law

Electrical resistance is the opposition to the flow of electric current in a conductor or circuit element. It is measured in ohms (Ω) and is represented by the symbol R. The relationship between voltage (V), current (I), and resistance (R) is described by Ohm's Law:

V = IR

This fundamental equation states that the voltage drop across a resistor is directly proportional to the current flowing through it and the resistance of the resistor itself.

Factors Affecting Resistance

The resistance of a conductor depends on several factors:

• Length: Resistance is directly proportional to the length of the conductor.
• Cross-sectional Area: Resistance is inversely proportional to the cross-sectional area of the conductor.
• Material: Different materials have different resistivities, which determine their resistance for a given length and cross-sectional area.
• Temperature: For most metallic conductors, resistance increases with increasing temperature due to increased vibration of atoms.

The resistance (R) of a conductor is given by the formula:

R = ρ(L/A)

Where ρ (rho) is the resistivity of the material, L is the length, and A is the cross-sectional area.

Electrical Energy and Power

Electrical energy is the energy transferred by an electric current through a circuit or device. It is measured in joules (J) or kilowatt-hours (kWh).

The electrical power (P) is the rate of energy transfer in an electric circuit. It is measured in watts (W) and is given by the formula:

P = IV

Where I is the current in amperes (A), and V is the voltage in volts (V).

In a resistive circuit, power can also be calculated using Ohm's Law:

P = I²R or P = V²/R

Worked Example

Problem: A 120 Ω resistor is connected to a 12 V battery. Calculate the current, power dissipated, and energy transferred in 5 minutes.

Solution:

• Given: R = 120 Ω, V = 12 V
• Using Ohm's Law, I = V/R = 12/120 = 0.1 A
• Power dissipated, P = I²R = (0.1)²(120) = 1.2 W
• Energy transferred in 5 minutes = Power × Time = 1.2 × (5 × 60) = 360 J

Efficiency in Electrical Systems

Efficiency is a measure of how effectively an electrical system or device converts input energy into useful output energy. It is expressed as a percentage or ratio of useful output power to input power.

The efficiency (η) of an electrical system is given by:

η = (Useful Output Power) / (Input Power)

Maximizing efficiency is crucial in electrical systems to minimize energy losses and improve overall performance.