Electrical Energy, Power, and Resistance in A Level Physics

Introduction

In A Level Physics, the topic of electrical energy, power, and resistance covers the fundamental principles governing the behavior of electrical circuits. Understanding these concepts is crucial for analyzing and designing electrical systems efficiently.

Electrical Resistance and Ohm's Law

Electrical resistance is a measure of the opposition to the flow of electric current in a conductor. It is governed by Ohm's law, which states that the current (I) flowing through a conductor is directly proportional to the potential difference (V) across it, and inversely proportional to the resistance (R). Mathematically, Ohm's law is expressed as V = IR.

Factors Affecting Resistance

The resistance of a conductor is influenced by several factors:

• Length: Resistance increases as the length of the conductor increases.
• Cross-sectional Area: Resistance decreases as the cross-sectional area of the conductor increases.
• Material: Different materials have varying resistivities, which determine their resistance for a given length and cross-sectional area.
• Temperature: Resistance generally increases with increasing temperature for metallic conductors.

Resistivity and Resistance Calculation

Resistivity (ρ) is a material property that quantifies the resistance of a specific material to the flow of electric current. The resistance of a conductor can be calculated using the formula R = ρL/A, where L is the length and A is the cross-sectional area of the conductor.

Worked Example

Problem: Calculate the resistance of a copper wire with a length of 5 meters, a cross-sectional area of 2 mm², and a resistivity of 1.7 × 10⁻⁸ Ω·m at room temperature.

Solution:

• Given: L = 5 m, A = 2 mm² = 2 × 10⁻⁶ m², ρ = 1.7 × 10⁻⁸ Ω·m
• Using R = ρL/A, substitute the values: R = (1.7 × 10⁻⁸ Ω·m)(5 m) / (2 × 10⁻⁶ m²)
• R = 4.25 × 10⁻² Ω = 0.0425 Ω

Electrical Energy and Power

Electrical energy is the energy transferred by an electric current flowing through a resistance. The power (P) dissipated by a resistor is given by P = IV or P = I²R = V²/R. The energy (E) dissipated over a time period (t) is E = Pt.

Efficiency in Electrical Systems

In practical electrical systems, some energy is inevitably dissipated as heat due to resistance. The efficiency of an electrical system is the ratio of the useful power output to the total power input, expressed as a percentage. Maximizing efficiency is crucial for optimal energy utilization and minimizing energy losses.