Electrical Energy and Power - Comprehensive Notes

Electrical Energy Transformation

Electrical energy can be transformed into radiant, thermal, and mechanical energy.

Using Electrical Energy

Essential Questions

  • How is electrical energy transformed into thermal energy?

  • How are electrical energy and power related?

  • How is electrical energy transmitted with minimal thermal energy transformation?

Vocabulary

  • Thermal energy

  • Superconductor

  • Kilowatt-hour

Electrical Energy, Resistance, and Power

  • Energy supplied to a circuit has various applications.

  • Motors convert electrical energy into mechanical energy.

  • Lamps convert electrical energy into radiant energy.

  • Hot plates convert electrical energy into thermal energy.

  • All devices convert some electrical energy into thermal energy.

  • Current moving through a resistor causes it to heat up because flowing electrons bump into the atoms in the resistor.

  • These collisions increase the atoms’ kinetic energy and, thus, the temperature of the resistor.

  • Household appliances act like resistors when they are in a circuit.

  • When charge (qq) moves through a resistor, its potential difference is reduced by an amount (ΔV\Delta V). The energy change is represented by qΔVq \Delta V.

  • The power dissipated by a resistor is given by:
    P=qΔVtP = \frac{q \Delta V}{t}

  • Since I=qtI = \frac{q}{t}, the power dissipated by a resistor can be written as:
    P=IΔVP = I \Delta V

  • Substituting ΔV=IR\Delta V = IR and I=ΔVRI = \frac{\Delta V}{R}, we get:
    P=I2R=(ΔV)2RP = I^2 R = \frac{(\Delta V)^2}{R}

  • A superconductor is a material with zero resistance.

  • There is no restriction of current in superconductors, so there is no potential difference (ΔV\Delta V) across them.

  • Because the power dissipated in a conductor is given by the product IΔVI \Delta V, a superconductor can conduct electricity without loss of energy.

Example Problem

A water heater operates at 240 V, and the resistance of its heating element is 12 Ω. How much current does it demand, and how much thermal energy will it produce in 30 minutes?

  • Knowns:

    • ΔV=240 V\Delta V = 240 \text{ V}

    • R=12ΩR = 12 \Omega

    • t=30 min=1800 st = 30 \text{ min} = 1800 \text{ s}

  • Unknowns:

    • I=?I = ?

    • E=?E = ?

Solution

  1. Use the relationship among current, potential difference, and resistance:
    I=ΔVR=240 V12Ω=20 AI = \frac{\Delta V}{R} = \frac{240 \text{ V}}{12 \Omega} = 20 \text{ A}

  2. Use the relationship among energy, current, resistance, and time:
    E=I2Rt=(20 A)2(12Ω)(1800 s)=8.64×106 JE = I^2 R t = (20 \text{ A})^2 (12 \Omega) (1800 \text{ s}) = 8.64 \times 10^6 \text{ J}

Providing Electrical Energy

  • Power is the rate at which energy is delivered.

  • Consumers pay for electric energy, not power, on their home electric bills.

  • A kilowatt-hour is equal to 1000 watts delivered continuously for 3600 s (1 h), or 3.6×106 J3.6 \times 10^6 \text{ J}.

  • Energy often must be transmitted over long distances to reach homes and industries, and it is desirable that the transmission occur with as little loss to thermal energy as possible.

  • To reduce this loss, either the current (II) or the resistance (RR) must be reduced.

  • Because the loss of energy is proportional to the square of the current in the conductors, it is more important to keep the current in the transmission lines low.

  • The current is reduced without the power being reduced by an increase in the voltage. Some long-distance lines use voltages of more than 500,000 V.