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. What’s the PE of an object with a mass of 5 kg? How about 10 kg?. Electrical PE.

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Electricity!

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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. • What’s 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

Let’s go back to the ladder • Potential due to gravity at 2 meters… • Is equal to 9.81 m/s2 x 2 m x the mass • Or… at 2 meters: • The PE = 19.6 m2/s2 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

What’s it called? • Named after a strange Italian • Whose name was Antonio… • Volta! • Note that a Volt • Doesn’t tell us how much energy is present • Just how much energy per unit of charge

Volts don’t 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 • = (kq1/d2) x q2 x d • = kq1q2/d

What does this look like? E1 – field strength due to q1 at “d” q1 - Distance “d” + q2 PE = E1 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 = kq1q2/d • d = kq1q2/PE • d = 9x109Nm2/C2 x 4x10-6C x 4x10-6C/0.1 J • d = 1.44 m

Let’s clarify… • PEelec – electric potential energy • Volt is the potential energy per unit charge • AKA “Electric potential” • ΔV = “Potential difference”

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, don’t 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 0.835 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 = 0.835 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)

Ohm’s Law • V = iR • Voltage = Current x resistance volts = amps x ohms

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

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

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”

695 400 s 20 C A) 2.6 mA b) 1.6 x 1017 e- c) 5.1 mA 703 0.43 A 1.8 A A) 2.5 A b) 6 A 110 V 46 ohms A) 0.41 A b) 0.59 A Homework

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 • Let’s 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?

There’s more to power… • P = Vi • V = iR • What is Power in terms of i and R? • P = i2R • In terms of V and R? • P = V2/R

Aha! A 75-watt light bulb! • V = 120 V • Determine i and R • I = 0.625 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?

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 = iReq • Req – resistance that the battery “sees” • Req = R1 + R2 + R3 … • For however many there are

What’s that mean? • Current only has one path • Doesn’t 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

Let’s look at one: • 100 volt system • 4 resistors • 5 Ω • 10 Ω • 15 Ω • 20 Ω • What is the total resistance? • Req = ???