Power, energy and efficiency

In this lesson, we will learn:

• How we can understand power as the rate of energy transformation.
• The definition of power related to energy and the 3 version of the power formula (related to voltage, current, and resistance)
• About energy as a property and the accumulation of power dissipation across a span of time that the circuit/device is operating
• How power is related to the efficiency of an electric circuit.
• How to solve for power, energy, and efficiency using:
• The formula for power: $P = IV = I^{2}R = \frac{V^{2}}{R}$
• The formula representing the relationship between energy and power: $P = \frac{E}{t}$ and $E = Pt = IVt$
• The efficiency formula: $efficiency = \frac{P_{output}}{P_{input}} x\,$100%

• Power is the rate at which energy is transformed (when the resistor/device transforms electric energy into another form of energy such as heat, light, etc.)
• Thus, power is defined as:
• $P = \frac{E}{t}$
• Where:
• $P$ is the power dissipated (in watts, W)
• $E$ is the energy transformed (in joules, J)
• $t$ is the time that the device/circuit is operating (in seconds, s)


• The unit for power is in watts (W) which represents: 1 Watt = $\frac{1 \, Joule}{1 \, Second}$


• Power can also be conceptualized as the product of current and voltage, giving the first power formula:
• $P = IV$
• The formula can be written in two other versions by substituting of Ohm’s Law into the power formula:
• $P = I^{2}R$ and $P = \frac{V^{2}}{R}$
• Energy is the property of the ability to do work (where work refers to energy transferred to objects in order to move them, heat them up, etc.)
• Energy is defined through rearranging the first power definition; energy is the accumulation of power dissipation for a duration of time:
• $P = \frac{E}{t}$ therefore, $E = Pt$
• And by substituting $P = I V$ (the power formula), it is given that: $E=I V t$
• The unit for energy is in joules (J) which represents a variety of physics concepts (gravitational potential energy; force and work; charge and voltage; power and time):
• $J= \frac{(kg)(m^{2})}{s^{2}} = Nm = CV = Ws$
• For your monthly electricity bill, you pay for energy (and NOT power). You are paying for how much energy you’re using by keeping your electronics on for an amount of time (power is the rate at which your devices are transforming electrical energy). You are not billed for the number of joules, but rather in the units of kilowatt-hours (1kWh = 3.6x10⁶J).


• The efficiency of an electric circuit is a percentage that represents the proportion of power that is produced by a device (useful output of dissipated power) over how much power is actually supplied to that device (input power that is consumed):
• $efficiency = \frac{P_{output} }{P_{input}} x$ 100%
• The efficiency is not perfect (100%) because there is energy loss when electrical energy is transformed into other forms (i.e. a lightbulb transforms electrical energy into thermal energy to heat up its wire filament so that it will glow and produce light energy; the initial heating is lost partially to the environment).