# Power, energy and efficiency

##### Intros

###### Lessons

##### Examples

###### Lessons

**Solving for Power and Resistance****Solving for Power, Current and Energy****Solving for Power and Voltage****Solving for Power and Efficiency**

An electric crane runs off of a 100V source at a current of 14A. The crane lifts a 180kg block 17.5m in the air (vertically) in 35 seconds. What is the efficiency of the crane?**Solving for Power and Efficiency**

A lightbulb emits approximately 300 J of light energy in 5 seconds. If this bulb is 16% efficient, what is the power supplied to the lightbulb?

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###### Topic Notes

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%

__Notes:____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 = 3.6x10^{6}J). - 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).

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