**History**Edit

No, Ohm's law has nothing to do with calm humming or yoga whatsoever. Rather, Ohm's law is a relationship vital to the understanding of circuitry. Ohm's law was formulated by German scientist Georg Simon Ohm who discovered that the ratio of the potential difference (the voltage drop from one point to a second point) to the current is constant for any conductor. In other words, the resistance remains the same as the magnitude or the direction of the potential difference changes. Initially Georg Ohm used voltaic piles, but later used a thermocouple because the thermocouple was a more stable voltage source, finally, to measure current he used a galvanometer. He applied various voltage levels to his circuit and recorded the resulting current. Through his experimental data he observed that the voltage drop was directly proportional to the current. This means that if voltage is plotted against current, the data will resemble a straight line where the slope at any given point is the resistance of the conductor. Ohm's law first appeared in his book *Die galvanische Kette, mathematisch bearbeitet* in 1827 in which he gave his complete theory of electricity. Other physicists did not readily accept his results because his law was based entirely on experimental data. Ohm was forced to resign from his teaching position and lived in poverty and shame. However, his work was eventually recognized by the Royal Society with its award of the Copley Medal in 1841.

http://www.corrosion-doctors.org/Biographies/images/ohm.jpg This image was taken from [1]

#### **R = V / I**Edit

###### *Definition of terms in the equation*Edit

R, Resistance, is the opposition that a material offers to the passage of an electric current. Resistance (measured in ohm’s) determines how much current will flow through a component. A resistor is a device that uses electricity to do work such as a light bulb, a hair dryer, or a microwave. Resistors can also be used to control voltage and current levels. A very high resistance allows a small amount of current to flow. A very low resistance allows a large amount of current to flow.
This image was taken from[[2]]

V, Voltage, is the difference in electrical potential between two points in a circuit. It's the push or pressure behind current flow through a circuit. Voltage comes from various sources that provide electric current; examples of these sources are batteries and electrical outlets.
This image was taken from [[3]]

I, Electric current, measured in amperes or amps, is a flow of charged particles through a circuit. Electric current is like the current of water flowing down a river in that both measure the quantity of matter traveling over a certain measurement of time. Current flows from points of high voltage to points of low voltage on the surface of a conductor. In circuits, current usually travels through wire.
This image was taken from [[4]]

The resistance of a conductor, R, is measured in Ohms represented by the symbol omega Ω and is defined as the ratio of the potential difference, V, to the current, I. One ohm (1Ω) is the resistance that permits a current of 1 A to flow when a potential difference of 1 V is applied across the resistance. Resistance can be thought of as the energy needed to move matter through a pipe for example. A clogged pipe will have more resistance than a clean one will.
**R = V / I**

Note: If you are planning to take the SAT II in physics, this equation should be memorized and you should be fluent with all aspects of Ohm's law. You will definitely see this topic on the test.

From this equation we can extract some useful facts:

- I is indirectly proportional to R, therefore, more resistance results in less current flow.
- V is linearly proportional to I, therefore, more voltage will result in more current flow.
- R is independent of V, therefore, it is a constant and cannot be changed.

In simple terms, a steady increase in voltage, in a circuit with constant resistance, results in a constant linear rise in current.

In this graph of voltage vs. current, as current increases voltage does also. This idea is intuitive; imagine your faucet is slightly clogged, by increasing the voltage or energy used to pump water through the pipes, water would come out of the faucet at a faster rate. You should also take note that the slope of the graph is the resistance of the conductor. At any given point the ratio V/I is equal to a constant resistance, R.

**Circuits**Edit

Ohm's law is very useful in solving simple circuits. The definition of the word circuit is " closed path". An electrical circuit is a configuration where electric charges travel in a closed path. A simple circuit requires three things:

- A source of electrical potential difference or voltage.
- A conductive path which would allow for the movement of charges.
- An electrical resistor

An electric circuit can be as simple as a battery, which provides voltage, and a single resistor such as a light bulb connected by wires.

###### *Circuit Symbols*Edit

In circuitry we use symbols to represent components of a circuit. Become familiar with these symbols as you may be asked to draw a circuit using circuit symbols.

###### **Series Connection** Edit

One of the most challenging tasks during the holiday season is managing to keep all the bulbs on holiday lights intact because when one bulb burns out the whole string of lights will remain unlit. This happens because the lights are arranged in series. This means that the electrical current has one choice of path. It can only travel through the circuit in one way, if this path is obstructed, the entire path will stop operating.

**In series these relationships hold true:**

I = I_{1} = I_{2} = I_{3} ...

V = V_{1} + V_{2} + V_{3}...

R_{Total} = R_{1} + R_{2} + R_{3}...

This diagram represents a series circuit:

Using the information given in this diagram can you determine the reading on the ammeter? Yes you can! Using Ohm's law, R = V/I, we first write out known values. We are told the voltage of the battery is 12V and the resistor is 2 Ω, therefore 2Ω = 12V/ I. When we solve for I we get 6Ω as the current. The ammeter will detect a current of 6Ω.

If the current of the circuit is 10 amps, what is the voltage of the battery?

This circuit may seem complex but we can use the relationships above and Ohm's law to solve the circuit.
First determine the total resistance of the circuit. This is calculated using the formula : R_{Total} = R_{1} + R_{2} + R_{3}...
, so the sum of the two resistors in the circuit equals the total resistance. Since 4Ω + 2Ω is 6Ω,the total resistance is 6Ω. Using the formulas above we must also take note that the current is equal throughout a series circuit and we are given the information that the current is 10. Now we use Ohm's law to calculate the voltage: R = V/I, 6Ω = V/ 10, so the voltage of the battery in the circuit is 60V.

**Parallel Connection**Edit

Is your house wired in series or parallel? Think back to the example of holiday lights. From this example we learned that in series when a resistor is unplugged or destroyed none of the resistors in the circuit will function. Let's say you unplug your hair dryer, do all the other appliances in your house turn off? I sure hope not! Our houses are wired in an arrangement called parallel. In series, all the resistors cease to function when one is destroyed because the electrical current has no choice of path in the circuit. The critical difference between a series and parallel circuit is that the electrical current in series has no choice of path whereas in parallel the electrical current can travel through the circuit in various paths.

**In a parallel circuit these relationships hold true:**

I = I_{1} + I_{2} + I_{3} ...

V = V_{1} = V_{2} = V_{3}...

1/ R_{Total} =1/ R_{1} + 1/R_{2} + 1/ R_{3}...

This is a diagram of a parallel crcuit. The current can travel through the 3Ω resistor or the 6Ω resistor as it goes through the circuit.

Using these formulas we can solve for the current of the circuit
First we can calculate the equivalent resistance of the circuit using this formula: 1/ R_{Total} =1/ R_{1} + 1/R_{2} + 1/ R_{3}...
1/ R total = 1/6Ω + 1/3Ω = 1/2Ω so the total resistance is 2 Ω
The voltage is 24V throughout the circuit so we have enough information to use Ohm's law to solve for the current of the circuit. 2Ω = 24V / I. The current of the circuit is 12 amps.

In this circuit what is the reading on the ammeter? To answer this question we must first use the formula for total resistance. 1/ R total = 1/60Ω + 1/40Ω+ 1/30Ω+ 1/20Ω = 1/8Ω. The total resistance is 8Ω Using this information along with the voltage of the battery we can use Ohm's law to solve for the current. R = V/I , 8Ω = 56V/I , I = 7 ampere. The current reading is 7 ampere.

**Non-Ohmic Conductors**Edit

Not all conductors obey Ohm's law. In fact, most conductors of electricity are non-ohmic conductors. Ohm's law is only true for resistors whose resistance does not depend on the applied voltage, which are called ohmic devices. Temperature is an important factor in determining the accuracy of Ohm's law. When the temperature of the metal increases, the collisions between electrons and atoms increase. When a substance heats up because of electricity flowing through it, the resistance will increase thereby defying Ohm's law, which states that resistance is a constant. With non-ohmic conductors, resistance depends on voltage and is no longer a constant. To determine whether a material is ohmic or not, one can plot voltage versus current and observe whether the data follows a linear path. At very high currents, the material may overheat and melt, causing an open circuit. At very high voltages, the material may be damaged by electric breakdown or arcing, causing a term most of us have heard of but never really understood, a short circuit. Some materials have resistances that change with magnetic field intensity, light intensity or other variables.

The resistance of a conductor depends on:

- The nature of the material
- The temperature
- The shape of the conductor

Keep in mind these non-ohmic conductors

- Batteries
- Semi-conductors
- Light bulbs
- Capacitors

## **Practice Problems**Edit

Regents level questions:

1)A For any point on the line, what does the ratio of V to I represent?

2) When a conductor has a potential difference of 100 volts placed across it, the current through it is 5 ampere. What is the resistance of the conductor?

3) A generator supplies current in a circuit. If the resistance in the circuit is increased, the force required to keep the generator turning at the same speed is

(1) decreased (2) increased (3) unchanged

4) If the potential difference across a 50- ohm resistor is 5 volts, what is the current through the resistor?

(1)10A (2) .5A (3) 5A (4) .1A

5) If the voltage across a 4-ohm resistor is 12 volts, the current through the resistor is

(1) .25 A (2) .48 A (3) 3.0A (4) 4.0A

6) A resistor carries a current of .1 ampere when the potential difference across it is 5 volts. The resistance of the resistor is

(1) .02 Ω (2) .5Ω (3) 5Ω (4) 50Ω

7) If the potential difference across a 12-ohm resistor is 6 volts, the current through the resistor is

(1) .33 A (2) .5A (3) 3 A (4) 4 A

8) Draw a circuit diagram to include a 60-V battery, an ammeter, and a resistance of 12.5 Ω in series. Determine the reading on the ammeter.

9)

(a) What is the total resistance of this circuit?

(b) What is the current of the circuit?

10) An 8Ω resistor is connected to a 20V battery. How much current is produced?

11) As the temperature of a coil of copper wire increases, its resistance

12) If the voltage across a 3Ω resistor is 12 volts, what is the current through the resistor?

13) If the voltage across a 40Ω resistor is 10 volts, what is the current through the resistor?

14) If four resistors each of 7Ω are connected in series, find the total resistance.

## Resources and ReferencesEdit

*Resources*Edit

http://micro.magnet.fsu.edu/electromag/java/ohmslaw/

I strongly suggest you visit this site. On this site you can fiddle around with a circuit for hours and discover Ohm's law with your own experimental data just like Georg Ohm himself!!

http://www.grc.nasa.gov/WWW/K-12/Sample_Projects/Ohms_Law/ohmslaw.html

This site has lots of regents level practice problems

http://www.angelfire.com/pa/baconbacon/page2.html

This site is perfect for students with dominant math skills. The site even has an Ohm’s calculator!

http://www.physics.uoguelph.ca/tutorials/ohm/Q.ohm.intro.html

This site gives a brief explanation on Ohm’s law but has cool experiments and a self-test.

http://en.wikipedia.org/wiki/Ohm's_law

This site is for the Ohm’s expert it explains Ohm’s law very thoroughly and also gets into more complicated aspects of Ohm’s law such as the continuum form of Ohm’s law.

http://www.collegeboard.com/student/testing/sat/lc_two/phys/phys.html?phys

This site is ideal for SAT 2 physics preparation.

http://www.funtrivia.com/trivia-quiz/SciTech/Ohms-Lore-212878.html

This is a practice test on Ohm's law, it has some cool questions on it.

https://www.allaboutcircuits.com/textbook/direct-current/chpt-2/voltage-current-resistance-relate/

This is a really good article on how voltage, current, and resistance relate.

*References*Edit

Glencoe Physics- Principles and Problems, by Paul Zitzewitz. Glencoe/McGraw-Hill, 1998.

This textbook gives clear explanations with a variety of problems to practice from and also offers informative experiments that can often be done with household materials.

Barron's Regents Review for Physics, by Miriam A. Lazar, third Edition. Barron's Educational Series, Inc. 2004.

This review book is like a bible to students studying for the physics regents. It clearly explains all the topics on the regents curriculum and gives realistic practice problems with two actual New York State Regents exams.

http://jersey.uoregon.edu/vlab/Voltage/

This website offers an experiment that allows you to apply various resistors and voltage to a circuit. If you apply too much resistance to the circuit, the light bulb will receive too much current and will break if you apply too little, the light will not turn on resistance. Test your knowledge of Ohm's law by trying to apply the right amount of voltage and resistance to get the light bulb to light up!

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

This website offers a clear explanation of Ohm’s law and also explains current law and voltage law.

http://www.kpsec.freeuk.com/ohmslaw.htm

Here you will find a concise explanation of Ohm’s law with helpful tips for answering questions.

http://www.regentsprep.org/Regents/physics/phys03/bsimplcir/default.htm

This site offers an explanation on the simple circuit and ohms law from New York state high school regents exam prep. This site is ideal for students studying for the physics regents.

http://www.sciencejoywagon.com/physicszone/lesson/otherpub/wfendt/ohmslaw.htm

A lesson on Ohms law from New York state regents prep site.

http://www.sparknotes.com/testprep/books/sat2/physics/chapter14section3.rhtml

If your studying for the SAT II in Physics, this site covers all the topics using clear explanations.