Electrical Circuits Application

While electrical circuits themselves are used everywhere in our everyday lives, the concepts behind electrical circuits have led to the practical use of safety devices such as circuit breakers. Circuit breakers that are used at the distribution board in houses are called MCB's or miniature circuit breakers. Essentially, breakers limit the current which can flow through a circuit. In a breaker, the heating effect on a bimetallic strip causes it to bend and trip a spring-loaded switch. Typically a single circuit is limited to 20 amperes, although this can vary. When there is a short circuit, which creates a large surge of current, a small electromagnet consisting of wire loops around a piece of iron will pull the strip, separating the contacts and breaking the circuit. After the fault causing the short circuit is repaired, the contacts can be pushed together by lifting a switch on the outside of the circuit breaker.

http://www.gcsescience.com/pme8.htm

Electrical Circuits Reflection

This unit was different from the others because we started off with a virtual lab. This virtual lab helped to show us Ohm's Law, which is V=IR with V being voltage (volts), I being current (amps) and R being resistance (ohms). This is the equation we use to solve circuits. The virtual lab helped us see the relationship between the three components. During the lab, we noticed that as the voltage increased, the brightness of the light bulb increased. Alternatively, the current decreased, as the resistance increased. This means that I  V and I  1/R.

Shows Ohm's Law (V=IR)
http://phet.colorado.edu/en/simulation/circuit-construction-kit-dc

Current is moving electrons, which also means that it can be represented as C/S or coulomb per second. The unit for current is known as an ampere. Increasing the current causes more electricity to move through the device as seen using Ohm's Law. Voltage is electrical potential, as we know from the previous unit. This also refers to how much work a battery in a circuit can do.The unit for voltage can be represented as J/C or joules per unit charge, which is also known as a volt. As current and voltage are directly proportional, the greater the current, the more voltage. Lastly, resistance slows down the current due to collision of electrons with atoms of the material they are passing through, which causes them to lose energy. As the resistance of a circuit increases, the current decreases as seen through the relationship of I  1/R.

There are 2 types of circuits that we studied, series and parallel. Series circuits are connected so that current passes through each element in turn without branching off. For parallel circuits, the current can only flow in one path, therefore the current stays constant throughout the entire circuit. Parallel circuits are a closed circuit in which the current divides into two or more paths before recombining to complete the circuit. Because there is more than one path for the current to flow, the current splits at nodes or junctions, which is any point where the current can split. This also means that each branch is independent from each other, which also means that the voltages across each branch are equal.

We also completed another virtual lab where we learned how the total resistances of circuits changes depending on whether it is a series or parallel circuit. The first thing we noticed in this lab was that when we added an additional lightbulb to our original circuit, the lightbulbs were both dimmer, and the current decreased. For series circuits, the total resistance of the circuit can be found by adding values for all the resistance together. This relationship can be seen as Req (total resistance) = R1+R2... However for circuits in parallel, the relationship between 2 resistance in parallel in relation to the total resistance of the circuit can be shown as 1/Req=1/R1+1/R2.

The next principle we learned to apply to solving circuits were Kirchhoff's Voltage Law and Kirchhoff's Current Law. Kirchhoff's Voltage Law is based on the conservation of energy, where the total amount of energy gained per unit charge (voltage gained) must be equal the amount of energy lost per unit charge (voltage dropped) as both energy and charge are both conserved.

As shown by the voltmeter, the voltage drop over each light bulb is 4.50 V which when added together, equals the voltage of the battery (9.00 V).

For Kirchhoff's Current Law states that at any node or junction in an electrical circuit, the sum of currents flowing into that node is equal to the sum of the current flowing out of that node. Therefore  I in =  I out.

Using these concepts we are able to solve both series and parallel circuits. For series circuits, we must first find the total resistance of the circuit, which is a concept we learned through the virtual lab by adding the resistances together. With this, we are able to solve for the total current of the circuit if we already know the voltage the battery produced. Since we know that the current stays constant through a series circuit, we can now solve for each voltage drop over each resistance in the circuit by using the total current, and the resistance to solve for V(V=IR). With our knowledge of Kirchhoff's Voltage Law, once we find each individual voltage drop, we know we have correctly solved the circuit by adding each voltage drop together, which should equal the voltage produced by the battery.

For parallel circuits, we can find the total resistance of the circuit by using 1/Req=1/R1+1/R2... to once again find the total current of the circuit. With the total current we can find the voltage drop using V=IR. Once we have found the total current of the circuit and the voltage drop, we can expand backwards to find how the current splits. Since the voltage across each branch is the same, we can solve for I using the individual resistances and the voltage for each branch.

The next concept we learned about was electrical power. As we learned, when a charges flows through a resistor, it loses energy due to collisions with the atoms in the wire. This energy loss is transformed into heat energy and is related to voltage drop since V=PE/q. Because power is the rate of doing work at which energy is transformed, Joules Law states that P=VI. In addition P=I^2R or P=V^2/R. To further extend this, we can also find electrical energy, since E=P(t) where t is time. Since a joule is a very small unit, we can use the kilo Watt-hour to represent energy. With being able to solve parallel and series circuit, we could also solve combination circuits, which combine principle from being able to solve both types of circuits.

The last section of this unit we learned was terminal voltage. Terminal voltage is the voltage (potential) difference between the terminals of a battery when connected to a circuit. This is because the battery contributes to some resistance to a circuit, also known as internal resistance. Where terminal voltage is the actually voltage that goes through the circuit, electromotive force or EMF is the maximum voltage that the battery can produce. When a cell is specifically being charged by another cell, the current flows backward therefore Vt (terminal voltage) = E (EMF) + IR (internal resistance), however when the cell is supplying current to the circuit, Vt = E - IR.

http://tap.iop.org/electricity/emf/121/page_46054.html

The most difficult part to this unit was just being able to and knowing when to apply each concept. When it came to the point where we were combining solving combination circuits, while having to use electrical power and electrical energy, I found it more difficult to just remember when to apply each concept. However this became easier as we continued doing more practice problems, and I became more used to solving more complicated problems.

Electrostatics Application

One common use of electrostatics is in laser printers. Laser printer use a process called xerography which applies some of the concepts used in electrostatics. This process involves a selenium coated aluminum drum, which is sprayed with positive charges from points on a device called a corotron. In the first stage, the conducting aluminum drum is grounded so that a negative charge is induced under the thin layer of positively charged selenium. In the next stage, the surface of the drum is exposed to the image of whatever is to be copied. Where the image is light, the selenium becomes conducting, and the positive charge is neutralized. In darker areas, the positive charge remains, and so the image has been transferred to the drum. The third and final stage takes a dry black powder, also known as toner, and sprays it with a negative charge so that it will be attracted to the positive regions of the drum. So, when a person wants to print on a blank piece of paper, it is fed through and the paper is given a greater positive charge than on the drum so that it will pull the toner from the drum. As the paper and toner passes through heated pressure rollers, it melts and permanently adheres the toner within the fibres of the paper.

http://cnx.org/content/m42329/latest/?collection=col11406/latest

Electrostatics Reflection

Electrostatics is the study of stationary electric charges or fields, as opposed to electric currents. This entails the forces acting on them and their behaviour in substances. Going back to Grade 9 Science, we reviewed insulators, conductors, and methods of charging objects. Insulators are materials in which the electrons are tightly bound to the nucleus, which means that they do not conduct electricity. Alternatively, conductors are materials in which the electrons in the outer part of the atom are free to move, which mean they conduct electricity. We learned of 3 ways to charge object, including friction, conduction and induction. Friction is when 2 objects are rubbed together and the electrons of 1 object transfer to the other. Conduction occurs when objects transfer electrons from touching, or making contact. Lastly, Induction is when a charged object is brought near, but does not touch a neutral object. Even though the objects do not touch, the charged object polarizes the neutral object and the electrons rearrange, therefore the object behaves as if it is charged, but is still electronically neutral.

The Law of Charges is that like charges repel and unlike charges attract. This is important to keep in mind when determining the direction a charges moves when in the presence of another charge. The Law of Conservation of Charge states that the net charge of an isolated system remains constant. The only way to change the net charge of a system is to bring in charge from elsewhere, or remove charge from the system. To describe the electrostatic interaction between electrically charged particles, we use Coulomb's Law. Coulomb's Law involves electric force (Fe), the universal constant (k), q (charge), and r (distance between the charges). Coulomb's law is Fe=kQq/r^2.

Next we learned about electric field, which is a vector quantity from which is determined the magnitude and direction of the force on a charged particle due to the presence of other charged particles. In comparison to gravitational force, they are both field forces, which means that no contact is necessary to influence an object. Although, a difference is that gravitational force is a weak force, while electrostatic force is a strong force. In addition, electrostatic force can be either attractive or repulsive due to the law of charges. Lastly, just as an object with mass has a gravitational field, a charged particle creates an electric field around it. To determine the direction of an electric field, we imagine that a small positive test charge is placed in the field, and depending on if the source is negative or positive, will move in different directions. To find the magnitude of an electric field, we can use the equation, E=kQ/r^2 or E=Fe/q, depending on whether the source charge is known, or the test charge is known.

An important skill we learned this unit was being able to draw a representation of an electric field. Electric field lines are used to show the electric field surrounding a charged particle.

http://www.alternativephysics.org/book/ElectricFields.htm

In the example above, we can see that the positive fixed charge has arrows coming out from it, while the negative charge has line going into it. We can also see that they are equal charges as the number of lines going in from the negative particle, equals the number of lines coming from the positive charge. In these diagrams, the number of lines also reveal the concentration of the electric field at a particular area. The more lines in an area, means the stronger the electric field. There are some specific rules for drawing these diagrams. Some of them are, that the lines must begin on positive charges, and end on negative charges, and no field lines can cross. 

The next concept we learned was electric potential energy. This is the energy stored in the system of 2 charges that are a certain distance apart. Electric PE reflects the work that must be done to move a small charge in an electric field created by a source charge. In this case, W (work) =∆PE (change in potential energy) which also equates to kQq/r. Because this depends on the distance or r, the PE is zero at an infinite distance. Unlike for electric force and electric field, we have to include the signs of the charges because unlike charges require negative PE as it takes work to separate the charges due to the attractive forces between the charges. 

Another slightly confusing topic we learned about was electric potential. Electric potential, also known as voltage is defined as the amount of electric potential energy per unit charge. The most difficult part about voltage is just recognizing that electric potential is the same as voltage when reading questions. The equation for electric potential is V (voltage) = PE/q, which also equals kQ/r. 

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elewor.html

The last type of problem we learned to solve is regarding parallel plates as seen above. An electric field is established between the two plates when they become charged, and they are connected by a battery. As you can see, one plate is positively charged, and the other is negatively charged. In addition, the electric field goes from the positive plate to the negative plate. Since the field lines are parallel to each other, the electric field is uniform in comparison to the electric field between point charges. Because the electric field between plates does not vary with the distance (as is the case with point charges), we can use the equation E=∆V/d to find the magnitude of the electric field. 

As I mentioned previously, I think the most difficult thing to grasp is when to use each equation. Just knowing what each question is asking for is something that took awhile to understand, however became easier with practice. 

Circular Motion Application

As I said in my previous post, I am going to expand on the physics behind Ferris wheels, and vertical circular motion in general. For Ferris wheels, it is important to first draw a free body diagram of the forces acting on a person sitting in the chair. It is also important to realize that the centripetal acceleration will still be in the direction of the center of the circle, therefore the magnitude of forces are different depending on whether you are sitting at the top or the bottom of the ferries wheel.

http://jesseenterprises.net/amsci/1983/10/1983-10-fs.html

If the person is sitting at the top of the rotation, there are 2 forces acting on the person, gravitational force (Fg) and normal force (Fn). At the top of the circle, the centripetal force (Fc) is downward, into the center of the circle. In the previous post, I wrote that Fc is the vector sum of all the forces on an object moving in circular motion. This means that Fn and Fg are not the same magnitude because Fg must be larger, as there is centripetal acceleration. 

http://www.chegg.com/homework-help/questions-and-answers/figure-shows-ferris-wheel-rotates-times-minute-carries-car-circle-diameter-180-m-force-mag-q2985616

In contrast, when the person is sitting at the bottom of the rotation, the Fc is upwards, which means that the magnitude of Fn is larger than Fg. This explains why on a ferris wheel, people feel light at the top, and heavy at the bottom. To solve these types of problems, we first need to recognize which force is larger, and then can use the equation for Ac to solve. For example, if the person is sitting at the top of the ferris wheel, Fc= Fn-Fg, which means that Fn=Fg+mAc, which proves that the top of the ferris wheel, Fn<Fg. 

Circular Motion Reflection

The next unit we studied this year was circular motion. Although I had learned some of the more simple concepts of this unit in grade 11, there were many new, challenging topics to learn. To begin with, we learned about uniform circular motion, which is when an object is moving with a constant speed in a circle, however it must be noted that the direction of motion is always changing, so the object is also accelerating. A demonstration in class showed that the direction of velocity is always tangent to the radius of the circular path, when a marble was swirled in a circular inside a roll of tape. When the tape was lifted and the marble continued to roll, it went straight in the direction it was moving without the circular path. This means that an object moving in a circle is accelerating toward the center of the path, and this is called centripetal acceleration.

When calculating the magnitude of centripetal acceleration (Ac) it is important to notice that the quantity is scalar because the direction of Ac is always towards the middle of the circle. The equation used for calculating this is Ac=v^2/r, where v is velocity, and r is the radius of the circle. If we are trying to find the total distance covered to complete one rotation of the circular path, we can find the circumference, by using v=2πr/T, where T is the period in seconds.

When solving problems with centripetal force (Fc), Fc is the sum of all the forces on an object moving in a circle, which means that it can include forces such as gravitational force or friction. Therefore, when we solve for Fc, we can expand to use Ac formula, leaving Fc=mAc=m(v^2/r).

Because many of the problems we do involve the Ac of cars turning corners, we also learned a practical application of this when we learned about banked curves. When you draw a free body diagram for a car turning a regular corner, we can see that friction is the centripetal force that keeps the car on the track. However, banked curves are when the surface itself is at an angle. This is much safer because it does not rely on friction to keep the car on the track. This means that cars can go faster on banked curves and be safe, while car will have to go slower around regular corners to be safe. The formula we use for banked curves is v=√rgtanθ, because θ is the angle of the curve, and we are using the parallel component of Fg to solve. While car problem involve horizontal circles, we also learned about vertical circular motion.

http://www.maa.org/publications/periodicals/loci/joma/banked-curves

Many of the example we do for vertical circular motion involve Ferris Wheels, which I will discuss in the application post, but just to get a general sense, Ac is still always in the middle of the circle, however, when an object is at the top of the circle, Fg and Fn are different than when the object is at the bottom of the circle.

The next part of circular motion that we learned was about gravitational circular motion, and orbital mechanics. From grade 11, we reviewed the Law of Universal Gravitation which is Fg=GMm/r^2, where G is the universal constant (6.67x10^-11). We also learned how to find the gravitational field strength that other planets exert on objects, such as Jupiter. To find this, we use g=GM/r^2.

A really important point to remember about this unit is that Fc=Fg when objects are in orbit. When we substitute formulas that we have already learned, we end up with m(v^2/r)=GMm/r^2, which leaves us with v=√GM/r. R in orbital mechanics,means the radius of the planet and the height at which the object is orbiting because the distance measured between object is from the center of each object.

The last section we learned was orbital mechanics. Orbital potential energy is relative, which means that the potential energy of an object changes depending on the reference point we are dealing with. To calculate potential energy (Ep) we use the formula, Ep=GMm/r. It is important to remember that for the potential energy of objects in orbit, the phrase "relative to zero at infinity" is used, which means that at an infinite distance from Earth means that the object's potential energy is 0. Therefore, when an object is closer to Earth, the potential energy is negative. When trying to find the amount of work done, we go back and use the conservation of energy, which is W=ΔKE+ΔPE. Escape velocity is when an object escapes the pull of gravity, and essentially travels an infinite distance from the planet. For this, we also use the conservation of energy, leaving Vesc=√2GM/r.

http://physics.nayland.school.nz/VisualPhysics/NZ-physics%20HTML/06_Gravitation/chapter6d.html

With this unit, the aspect that I had the most difficulty with was trying to derive the formulas required to solve for different values. For many of the problems we did, asked to solve for the radius or period, which there is no explicit equation to use to solve for. Instead, we had to substitute different equations in and derive the formula needed. Although this does not seem overly difficult, it was an adjustment that took a lot of practice to get used to doing in a timely manner. Another concept that I struggled to remember was that the term "radius" meant that the distance measured is from the center of the 2 object, and includes the height that the object is orbiting. Although I understand this, I sometimes forgot to include the appropriate heights when doing calculations.

Mobile Mechanics - Translational and Rotational Equilibrium