Understanding Electrical Energy, Power and Resistance

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 represented by th...

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 represented by the symbol R and has units of ohms (Ω). Ohm's law describes the relationship between potential difference (voltage), current, and resistance in an electrical circuit:

V = IR

Where V is the potential difference in volts (V), I is the current in amperes (A), and R is the resistance in ohms (Ω).

Factors Affecting Resistance

Length: Resistance is directly proportional to the length of the conductor. Longer conductors have higher resistance.
Cross-sectional Area: Resistance is inversely proportional to the cross-sectional area of the conductor. Thicker conductors have lower resistance.
Material: Different materials have different resistivities, which is a measure of their ability to resist electric current flow. Metals like copper and silver have low resistivity, while insulators like rubber and plastic have very high resistivity.
Temperature: For metallic conductors, resistance increases with increasing temperature due to increased vibrations of atoms in the lattice structure, impeding electron flow.

Electrical Energy and Power

Electrical energy is the energy transferred by an electric current through a circuit. It is calculated using the formula:

Energy = Power × Time

Electrical power is the rate at which electrical energy is transferred or dissipated. It is calculated using the formula:

Power = Current × Voltage

Power = (Voltage)2 / Resistance

Worked Example

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

Solution:

Using Ohm's law, V = IR, we can calculate the current: I = V/R = 12/120 = 0.1 A
Power dissipated = 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

In any electrical system, some energy is dissipated as heat due to resistance in the components. The efficiency of an electrical system is the ratio of useful power output to the total power input, expressed as a percentage. An ideal system would have 100% efficiency with no energy losses.