Electric Current and Power

Relation to Energy

We will focus on the elements of electric theory that are most closely related to the expenditure of energy in electrical systems.

Current

  • Current is the movement of electrons in a conductor
  • This has units of coulombs per second or amperes.
  • Water flow is a good mental model.

Alternating and Direct Current

  • Alternating current (AC) flows back and forth
    • The electricity supply to our homes is AC and has a frequency of 60 cycles per second
  • Direct current (DC) flows in one direction
    • The batteries in our phones and laptops use DC

Power Units

Any circuit element with a given voltage and current is consuming power equal to the product of the current and the voltage

The power being converted in a circuit is given by this formula.

The power converted by an electrical device is equal to the voltage across it multiplied by the current flowing through it.

P = VI

  • Voltage is energy per charge
  • Current is charge per time
  • Voltage times current has units of energy per time or power
  • If the voltage is in volts, and the current is in amperes, the resulting power is in units of watts.

\frac{energy}{charge} \cdot \frac{charge}{time} = \frac{energy}{time} = power

Visualization

On a graph with current and voltage, the area of a box with the origin in one corner and the current and voltage of the device in the other will have an area equal to the power in watts.

Energy in a circuit element

The energy consumed is equal to the power multiplied by the time.

To find the energy from this power we multiply power by time.

E = P \cdot t

This energy is expressed in watt-hours or kilowatt-hours.

  • A watt times an hour is a watt-hour.
  • A kilowatt times an hour is a kilowatt-hour. (This is the unit of electricity on your bill.)
  • A 1 kW device consuming power for 1 hour uses 1 kWh of electricity

We can also convert this to joules.

A watt times a second is a joule.

Energy Conversion

For the current to flow, there must be energy applied to the circuit and that energy must come from a source.

  • The chemical energy in a battery is converted into the electrical potential energy.
  • The chemical energy in coal is converted to heat and then to mechanical energy to power an electromagnetic generator that provides the electrical potential energy.
  • A solar panel takes the energy from one of the sun’s photons and converts it to electrical potential energy.

Paying for Electricity (Tariffs)

  • The utility charges proportional to the amount of kWh consumed
    • This is called a volumetric charge ($/kWh).
  • Some consumers are also charged according to the maximum average power observed over an interval of time (often 15 or 30 minutes)
    • This is called a peak charge or demand charged.

You can think of one as paying for the total amount of energy and the other as paying for the maximum amount of power delivered.