Discovering the relationship between voltage and revolutions per minute of an electric fanExplorationAim The aim of the the experiment is to discover the relationship between voltage, measured using a voltmeter and incremented by a variable resistor and the revolutions per minute of a wind fan, all connected on a DC motor. Introduction and hypothesisI was always curious on how the fan worked as a kid. This is because it looked so simplistic on its functioning, so I wanted to know how it work. When I went to few websites, I really didn’t understand the definitions of voltage and current. Now I understand that the definition of voltage is the difference in electric potential energy between two points per unit electric charge. The voltage between two points is equal to the work done per unit of charge against a static electric field to move the test charge between two points. This is measured in units of volts (a joule per coulomb). From this, we can deduce the equation of voltage is:V = WDQWhere:V =  Voltage (Volts)WD = Work Done (joules)Q = Charge(Coulombs)Revolutions per minute is measure of the frequency of rotation, the number of rotations around a fixed axis in one minute. However, how does the fan work?The Motor starts rotating as long as the current is running through the circuit. Then the Blades attached to the motor starts rotating. This in turn turns electrical energy into kinetic energy . After this, the fan produces wind with high pressure and low volume. This is where the torque force comes in.  The torque force is a rotational force. The definition of torque is that both of the angular velocity or inertia of an object changes constantly (uoguelph, What is Torque?). In order to understand the relationship between them, it has to be derived. Ohm’s Law states that the current through the conductor is directly proportional to the voltage and is expressed through the equation:I = VRWhere: I = Current(Coulombs)V = voltage(volts)R= Resistance()From this, you can calculate  resistance of your motor by measuring the current and voltage. For any given resistance (in the motors it is basically the resistance of the coil) this formula explains that the current can be controlled by applied voltage.The consumed electrical power of the motor is defined by the following formula:Pin = I VWhere:Pin = input power (Watts)I = Current (Ampere)Motors supposed to do some work and two important values define how powerful the motor is. It is motor speed and torque – the turning force of the motor. Output mechanical power of the motor could be calculated by using the following formula:Pout = where Pout – output power (Watts)? – torque (N/M)? – angular speed.(ms-1)The more the voltage is increased, the revolutions per minute will increase. This is because as voltage increases, the electrical energy produced also increases, therefore increasing the power of the wind fan. This is because work done = power x time, thus, increasing voltage indirectly increases the power to increase due to voltage = WD/Q.Independent variable Voltage: This is because voltage is not dependent on other variables and is provided from the voltmeter. Dependent Variable Revolutions per minute: the Revolution per minute is dependent on the voltage producedControl VariableControlHowWhyUse the same wind fanDon’t change the wind fanSome wind fans might perform differently from others. Use the same voltmeterDon’t switch/replace voltmeterSome voltmeters might read differently than others Use the same motorDon’t switch/replace motorOne motor is enough for your control variablesApparatusTachometerVoltmeter WindfanAC/DC MotorVariable resistorMethodConnect the Voltmeter, Wind Fan, and AC/DC motor in a circuitStart the variable resistor at a reasonably high resistanceTurn on the wind fan and let it run for ten secondsTurn on the tachometer and start calibrating the tachometer with the fan until 4 blades are visibly seen. Record the voltage and the revolutions per minuteDecrease the resistance using the variable resistor and repeat step 3 to 4.AnalysisResultsRevolutions per minute (RPM)10Voltage (V) 0.01Trial 1Trial 2Trial 3Average0.164304294314300.18557556556556.30.22725725724724.70.25835836836835.70.321070106910691069.30.361185118911891187.70.411376137413191356.30.451456146014571457.7Graph Conclusion As we can see here, the graph is a steep, straight line. This means that voltage does have a relationship with revolutions per minute. However, in order to find torque and angular speed, it is expressed in these equations. Using the variable resistor, we can also see that the higher the voltage, the higher the revolutions per minutes are. This experiment shows that even if the resistance is really small, the revolutions per minute will increase considerably. We can also see that the equation of the line is y = 3466x -65.9This therefore shows that the relationship is linear. This is because, as stated in the hypothesis, the voltage has a relationship with revolutions per minute, as the motor running the fan does increase the speed of the wind fan.  EvaluationIf the experiment was done again, there will be better apparatus used. The wind fan needs to be changed because the wind can in this experiment, did not work sometimes, and it therefore deterred the results. A new, powerful  fan could be used because the fan used in this experiment was pretty weak, therefore the results from the test was almost inconclusive. Another improvement should be the voltmeter. The voltmeter was a basic voltmeter, due to it being a old model, a new model could be required to measure the voltage. Crocodile clips need to be new because the ones used were rusted, therefore new crocodile clips is needed due to the rusting crocodile clip not working efficiently. The tachometer could be another new apparatus due to the tachometer not being really reliable. If we could redo the experiment, we would do it with new apparatus, and also take other variables into account, such as increasing the torque, (by introducing smaller fans).  Works CitedWhat Is Torque?, www.physics.uoguelph.ca/tutorials/torque/Q.torque.intro.html.”How Do Electric Fans Work?” It Still Works | Giving Old Tech a New Life, itstillworks.com/electric-fans-work-4564463.html.Howard, Damien. “What Is Torque? – Definition, Equation & Calculation.” Study.com, Study.com, study.com/academy/lesson/what-is-torque-definition-equation-calculation.html.