Electricity! February 22/23, 2010

Electrical Potential Energy Remember gravity? And gravitational potential energy? PE = mgh The higher you go the more PE you have… Consider the ladder at 2 meters high. Whats the PE of an object with a mass of 5 kg? How about 10 kg?

Electrical PE Electrical energy is very similar If we take a + charge and pull it away from a - charge We do work on it (force x distance) We create potential energy If you let it go Smaaackkk… It flies towards the - charge Making kinetic energy

Lets go back to the ladder Potential due to gravity at 2 meters… Is equal to 9.81 m/s 2 x 2 m x the mass Or… at 2 meters: The PE = 19.6 m 2 /s 2 x whatever mass you have The gravitational potential is equal to 19.6 J per 1 kg of mass No matter what you take up the ladder The PE is 19.6 J/kg x the mass (kg)

Electrostatics –big copy cat If you look at the potential energy per unit charge… PE/# charges In units of Joules per Coulomb This is the Electric Potential NOT Potential ENERGY For every Coulomb of charge at some location You get so many Joules of potential energy

Whats it called? Named after a strange Italian Whose name was Antonio… Volta! Note that a Volt Doesnt tell us how much energy is present Just how much energy per unit of charge

Volts dont kill Consider a raindrop a mile up in the air It has a lot of gravitational potential This is like voltage But not much mass Mass is like the charge

Which would you prefer? To be hit by a rain drop that started falling 1 mile up Or… Hit by piano that started falling 10 feet up? What is the connection to electricity?

Potential Energy – electrically speaking… PE = E x q x d This is like Force x distance Which is work Work done on an object gives it PE PE = E x q x d = (kq 1 /d 2 ) x q 2 x d = kq 1 q 2 /d

What does this look like? - + Distance d E 1 – field strength due to q1 at d q1 q2 PE = E 1 x q2 x d PE = k q1 q2 / d

Electric PE The electric potential energy between 2 charged objects is 0.10 J Each object has a charge of 4.0 x 10 –6 C How far apart are they? PE = kq 1 q 2 /d d = kq 1 q 2 /PE d = 9x10 9 Nm 2 /C 2 x 4x10 -6 C x 4x10 -6 C/0.1 J d = 1.44 m

Lets clarify… PE elec – electric potential energy Volt is the potential energy per unit charge AKA Electric potential ΔV = Potential difference

No difference in PE - so no flow of water (charge). Increase gh of one end…like voltage difference

Now for something more concrete…

No longer static Elements of electricity Voltage difference (V) Current (I) Resistance (R) Voltage weve already started to explore…

But we just got started! Now… lets measure some volts! The Electric Light Bulb

Electricity – closer to Ohm February 18/19, 2009 Circuits unplugged

Homework 2) 4.5 meters 4) 1.60 x 10 –19 C 2) position, charge, electric field strength 4) No, but usually choose reference point that sets initial PE = 0

Remember? Think, dont speak… What were the 3 parts of an electric circuit… Tell a neighbor or write it down Can you describe voltage?

Current Charge per time Like a charge flow rate Units of ampere amp Coulomb/second = 1 amp C/s

Current calculation The current in a light bulb is A. How long does it take for a total charge of 1.67 C to pass a point in the wire? ΔQ = 1.67 C I = A Δt = ΔQ/I = 1.67(C) / 0.835(C/s) = 2.00 s

Resistance This is why we want electricity… Measure in ohms (Ω)

Ohms Law V = iR volts = amps x ohms Voltage = Current x resistance

sooooo Voltage is proportional to Current and resistance How are… Current and resistance related?

12 volt battery 30 ohms of resistance What is the current? V = iR 12 V = i (30Ω) i = 0.4 A

Lets assume… Using the hand generators… And you generate 0.25 amps of current Resistor was 5.0 Ω What is the current?

Drawing circuits…

Current topics Moving charge must be 1 of 3 varieties: Positive Negative Both Current is defined as flow of positive charges

Against the tide… So if a positive charge is moving forward… That is like a negative charge moving backwards…

What is actually moving? When you set current in motion You really just cause electrons to bump into one another They pass along the energy without moving all the way Like dominos

Drift Velocity Turn on the light switch We see the effect at close to the speed of light But the electrons take much longer to move There is some random movement With an overall motion in the direction of the electric field This overall motion is called the Drift Velocity About 1 meter per hour

Sources of current Batteries Convert chemical energy into electrical energy Generators Convert mechanical energy into electrical energy Electric energy is converted into some useable form at the load

AC DC Alternating current Sine wave current (washing machine) Constantly changes sign – vibrates back and forth. Direct current Steady current at a particular voltage

Measuring voltage Always measure across a resistance or voltage drop The volt meter gets hooked up in parallel Hugs

Measuring current Always measure current in line The ammeter gets hooked up in series. Holds hands

Ohms Mill February 20/23, 2009

Homework s C 5. A) 2.6 mA b) 1.6 x e- c) 5.1 mA A A 3. A) 2.5 A b) 6 A V ohms 6. A) 0.41 A b) 0.59 A

Resistance Resistance is…well Resistance to the flow of charge Resistance increases when The length of the carrier increases The diameter of the carrier decreases The temperature increases It also varies with material

PE, Work & Power Lets look at a simple circuit And think about the energy transfers PE gained across the battery… Is lost across the resistor Voltage drop

How much Power? Power = work divided by time P = W/Δt =ΔPE / Δt ΔPE = qV So… P = Vq/Δt P = V i

Light bulb goes on… A 60 watt light bulb is turned on… The voltage of the system is 120 V What is the current? P = Vi I = P/V I = 60 W/120 V = 0.50 A How much resistance is in a 120W bulb?

Theres more to power… P = Vi V = iR What is Power in terms of i and R? P = i 2 R In terms of V and R? P = V 2 /R

Aha! A 75-watt light bulb! V = 120 V Determine i and R I = A 75 W = (0.625 A) 2 R R = 192 Ω

Higher watts means… Typically have a constant voltage… More or less current? Less or more resistance?

Now, on to Ohm…. Or… the disgraced high school teacher

Life and times Georg Simon Ohm: Bavaria in 1787 Defined relationship between voltage, current, and resistance. Dismissed by his colleagues. Ohm resigns from his high-school teaching position Lived in poverty and shame. And now…the inside story:

Ohm was a clever lad Had a small grain mill Powered by a waterwheel Ohm pondered the relationship of electricity in his Volta Battery Then one day…

The series connection A series circuit is like holding hands Electricity passes through each person One at a time Until it reaches the other side of the voltage source Total voltage of a series system V = iR eq R eq – resistance that the battery sees R eq = R 1 + R 2 + R 3 … For however many there are

Whats that mean? Current only has one path Doesnt get used up… Must have same value through entire circuit The resistors have to share voltage drop Energy used is proportional to resistance Total voltage drop = ΣV for all resistors The power will vary, too Follows voltage

Lets look at one: 100 volt system 4 resistors 5 Ω 10 Ω 15 Ω 20 Ω What is the total resistance? R eq = ???

Now about that power bill… What is the voltage drop across each resistor? What is the current flow? What is the power for the entire system? How about for each resistor?

Your turn… A 6 volt battery is hooked up to a 6Ω and 18 Ω resistor in series. What is the R eq What is the current in the system? What is the voltage drop across each resistor?

Lab To the table!

Electricity – Parallel Circuits February 24/25, 2009

Ohm work Ω 2. 58,000 Ω Ω A; 312 W Ω; 1.00 A; 1.00 A V; 2.0 V; 2.5 V; 3.5 V 4. a) Ω; 0.80 A b) 5.79 V; 3.2 V Ω

Series review If you add a resistor to the circuit What happens to the current? What happens to the total voltage? What happens to the individual voltages? Total resistance? Power?

Meanwhile back at the grain mill… Ohm figured out the series circuit… Like 2 loads on one water wheel Wanted to add another wheel for oats But it wouldnt fit… Parallel circuits didnt seem to follow the rules… Or did they???

Parallel circuits Water/current has multiple paths to follow It seeks the path of least resistance More flow where resistance is less More flow overall Total current is the sum of all individual currents i = i 1 + i 2 + i 3 + …

The parallel connection Voltage is the same for each water pipe in parallel V total = V 1 = V 2 = V 3 = … Each resistor sees the same potential difference [potential energy] What happens when one path is stopped?

You may see this in the lab… i = i 1 + i 2 + i 3 + … Substituting I = v/R v/R = v 1 /R 1 + v 2 /R 2 + v 3 /R 3 … And since v is constant 1/R eq = 1/R 1 + 1/R 2 + 1/R 3 …

Example 12 volt difference 2 resistors in parallel: R 1 = 2 Ω R 2 = 4 Ω R eq = ? i = ? (in each section and total) What happens when I add another resistor in parallel? (R = 6 Ω)

What happens when we add a resistor to the parallel circuit: To voltage? To current? To R eq ? To power?

Lab Demo parallel circuit set up. Where do the ammeters go?

Voltmeters Voltmeters – in parallel Does it have a big resistor or a small resistor?

Complex Circuits - intro What happens when we have a little of both?

Electricity – Complex Circuits February 26/27, 2009

Homework Ω 3. A) Req = 2.2 Ω B) 6 A, 3 A, 2 A 4. A) Req = 3.0 Ω B) 36 V C) 2 A; 4 A; 6 A

Voltmeters Voltmeters – in parallel Dont want it to affect the circuit… Increase current or affect voltage Does it have a big resistor or a small resistor?

Ammeter In series… Again – dont want it to affect the circuit… Big resistor or small?

Complex Circuits - intro What happens when we have a little of both?

Electricity – Review notes March 6/9, 2009

Short circuit? What is a short circuit? How does it differ from a break in a circuit?

What happens… To resistance if you add a resistor in series? In parallel? To current if you add a resistor in series? In parallel?

More The equivalent resistance of two identical resistors in parallel is… If you start with the situation above and increase the resistance through one of them…the total goes: What is the maximum resistance of 2 resistors in parallel?

Youve got the … Power! P = Vi = i 2 R = V 2 /R If the current goes up… The power???

If, then… You break a series circuit… You break a parallel circuit… In a complex circuit…

What is wrong with these… Meters, currents, etc.

WWWT