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.