# Power

Voltage and current are fundamental concepts in electronics and **power** is another important concept.

Power is the *rate* of energy **production** or **absorption** within a circuit. In physics it is defined as the **rate of work** performed per second **[J/s]**. In electronics it is the rate at which electrical energy is transferred in a circuit per second and has the SI unit of the **Watt [W]**.

**Power **is related to **voltage **and **current **with the following simple relationship:

From this we see that power is proportional to **voltage** and **current** which makes sense as we expect that more energy would be delivered to a load with a higher voltage and that higher currents would lead to higher energy being dissipated by a load.

A simple real life example of power and energy transfer is a heater where the electrical energy will be converted into heat.

## Derivation:

We can derive the above equation for power and other useful relationships from the basic concept of power being energy transfer per unit time:

From here we can determine relationships in terms of resistance by using Ohm's Law which can be very helpful to calculate power efficiently!

## Examples:

**1.** What is the power delivered by the voltage source in the circuit below?

**power**for this circuit, one of which is to first calculate the current and then multiply this by the voltage and another is to use the relationship we derived earlier directly which links power to voltage and resistance: Let's now use the first method to check :)

**2.** What is the power dissipated in a 200Ω resistor powered by a 5mA current source?

## The kW*hr Unit

**Kilowatt-hours** are something we commonly hear about from energy providers as it is the standard unit of energy they speak of.

For this unit, **power **is measured in **kW **and time in hours. For example **1kWhr** reflects a device drawing **1000W **in an hour but note that this can also be achieved by leaving a device on which draws **2kW **of power for half an hour. From this we can see how it is a convenient unit when comparing **energy usage**.

### Questions:

**1. a)** What is the power delivered by the voltage source in the circuit below?

#### Answer

**b)** What is the power dissipated in R1?

#### Answer

**c)** What is the power dissipated in R2?

#### Answer

**2. a)** What is the power delivered by the current source in the circuit below?

#### Answer

**b)** What is the power dissipated in R1?

#### Answer

**c)** What is the power dissipated in R2?

#### Answer

## Lab:

We can also measure the power dissipated in a resistor with LTSpice! Very nice indeed so let's try experimenting with that by constructing the circuit below:

We can then measure the **power dissipated** by **resistors **by simply hovering over them, the bottom left corner will then display the power dissipated! We can then see that we have 1.5625mW dissipated in R1, 3.125mW in R2 and 1.5625mW in R3 we can also then hover over Vs to observe the power it delivered which is 6.25mW which is **equal to the** **power dissipated in all of the resistors**.