View source for Power in a circuit

Short Description of Topic

==The Main Idea==
Measuring the power in a circuit can provide useful insight into the ability of a circuit to accomplish a given task. In order to understand how to calculate and interpret power in a simple circuit, one must know the mechanical definition and significance of [[Power]]. For this section, we will be using the unit of Watt for power. 

It is important to note that the power in parts of a circuit can be represented in several different ways. Most commonly, power in a circuit is expressed in terms of Voltage (E, Emf, Volts), Current (I, Amps), and Resistance (R, Ohms). It is typical to focus a discussion of power in a circuit around the power that is dissipated by a resistor. The power dissipated by a resistor directly coincides with the amount of energy that the resistor converts into non-electrical energy such as thermal or light energy.
===A Mathematical Model===

The power dissipated in a resistor is <math>P=IV</math> or <math> P=I^2R</math> or <math>P=V^2/R</math>

===A Graphical Model===
Here is a model of how the power dissipated changes as the resistance in a circuit is modified. This graph is based on a constant voltage of 12 volts.

[[File:Power_in_a_circuit.jpg]]

From the graph, it becomes clear that as resistance increases, the power dissipated by the resistor decreases.
This also graph models how using a potentiometer or variable resistor would effect the power dissipation in a 12 volt circuit.

==Examples==

3 varying examples.

===Simple===
A circuit with a steady voltage of 12 volts has a current of 5 Amps. How much power is dissipated by this resistor?

<math> P=VI=12*5=60</math> Watts 

===Middling===

A circuit with a steady voltage of 6 volts contains two resistors in series, one with a resistance of 4 ohms and one with a resistance of 7 ohms. How much power is dissipated by the circuit?

First, calculate the overall resistance of the circuit.

<math> R_1+R_2=R_f=7+4=11</math>  Ohms

Then we can use one of the above equations to calculate the power dissipation.

<math> P=V^2/R=6^2/12=3</math>  Watts

===Difficult===
A circuit switches from a power supply with 6 volts to a power supply with 12 volts, what is the change in power dissipation if the circuit contains two 4 Ohm resistors wired in parallel?

First, we calculate the total resistance of the circuit. Since the resistors are in parallel, we must use the equation: <math>1/R_t=1/R_1+1/R_2</math> 

so R_t=1/(1/4+1/4)=1/.5=2</math> Ohms

So, we can calculate the power difference by using the change in voltage and the total resistance.

<math>deltaP=(V_1-V_2)^2/2=(12-6)^2/2=36/2=18</math> Watts

==Connectedness==
This topic is extremely important in examining infrastructure related to energy distribution. For example, in power grids, power lines are resistors, and therefore dissipate a certain amount of power. Since resistance is also related to the length of a wire, we can deduce that more power will be dissipated across longer power lines.

Additionally, it is extremely important to understand the concept of power dissipated by a resistor in the field of Electrical Engineering. For example, knowing how to calculate the power dissipated allows for the calculation of how large a resistor needs to be in order handle the energy dissipated over time through heat.

==History==
The discovery of how to calculate the power in a circuit is directly related to the discovery of Ohm's Law which relates voltage to resistance and current.
Ohm's law was discovered by [[Georg_Ohm]]. 
The further development of the units for these three properties results in the derivation of the calculation for power dissipation in a circuit.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore?  How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===

Internet resources on this topic

==References==

This section contains the the references you used while writing this page

http://mechatronics.mech.northwestern.edu/design_ref/sensors/potentiometers.html
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elepow.html
https://openstaxcollege.org/files/textbook_version/low_res_pdf/9/CollegePhysics-LR.pdf
http://micro.magnet.fsu.edu/electromag/java/ohmslaw/


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