Ohm’s Law

Physics 102Professor Lee

CarknerLecture 14

PAL #13 Capacitors 0.005 C stored on capacitor at 1000 volts What is capacitance?

Q= CV C = Q/V = 0.005/1000 = 5X10-6 F = 5 F

Jury-rig a replacement out of metal foil and Teflon coating (k = 2.1, thickness = 0.01 mm). C = 0A/d A = Cd/0 = (5X10-6)(0.00001)/(2.1)(8.85X10-12) A = 2.69 m2

How can such a device be portable? Roll it up, making sure the foil won’t short

Consider a pair of metal plates separated by an air gap that acts as a capacitor. How could the amount of charge on the plates be increased for a given voltage?

A) Replace the air with vacuumB) Replace the air with a copper plateC) Replace the air with cardboardD) Increase the separation of the platesE) Use round plates instead of square ones

Why is a dielectric useful in a capacitor?

A) It keeps the plates from touchingB) It increases the conductivity of

the platesC) It increases the charge that can

be stored per voltD) a and c onlyE) a, b, and c

If the voltage across a capacitor is doubled, the amount of energy stored on the capacitor,

A) Is halvedB) Stays the sameC) Is doubledD) Is tripledE) Is quadrupled

Circuit Theory There are three key variables used in circuit

theory:

V provides energy and causes charges to move

Energy can be extracted from the current due to resistance (symbol: R)

Current The current is the flow rate of

charge and is defined as:I = Q/t

The current is carried by charged particles called charge carriers

Inside a Wire What goes on inside a current carrying wire? An applied potential difference makes them

want to move in a certain direction (against the field)

However, the electrons do not move in a straight line

Note that the electrons are not pushing each other, they just react to the potential

The direction of the current is opposite the

motion of the electrons Convention is based on the positive charge, but

protons don’t normally move

Resistivity If you apply the same V to several

different types of materials you get different currents Why?

They have different resistivities (symbol

)

Resistivity is a property of a particular type of material rather than of a particular wire

Resistance

The total resistance of the material also depends on its size

The resistance can be written as:R = (L/A)

The units of resistance are ohms (volts per ampere)

Simple Circuit

Ohm’s Law

How much current do you get if you put a potential difference V across a wire with resistance R?

I = V/R

This relationship is called Ohm’s Law Commonly written as:

V = IR Ohm’s law is very important, memorize it!

Every individual piece of a circuit obeys Ohm’s law

Temperature and Resistance

Electronic devices get hot! Temperature also affects electronic properties

This increased random motion means collisions are more frequent and it is harder for current to flow

Resistance generally increases with temperature

Energy in Electric Circuits

As the charges flow (as current) they convert the potential energy to kinetic energy

We should be able to relate the potential difference, current and resistance to the energy produced

Energy Dispersion Rate Each charge that passes through the battery

gains energy that it will later lose as heat

Each charge then gives up its energy so the total power (energy per second) depends on the rate of charge flow or current

V = P

Power Using Ohm’s law (V = IR) we can

write:

In general we will know the values of R (since it depends on the properties of the resistor) and V (since we should know the voltage of our source or battery)

Lightbulbs A common circuit element is the

lightbulb

Household lightbulbs are rated in watts

In the US, most power outlets produce 120 volts of potential difference

Those that do not use a transformer

Conservation of Charge

If a current flows through a single wire, the value of the current must be the same everywhere

Otherwise charge would be gained or lost

Conservation of Energy Each resistor has a V associated with it

The sum of the voltage drops across all circuit elements on a single wire must be equal to the potential difference across the ends of the wire

All wires connected between the same two points must have the same V Since the change in potential energy is the same for

each

Resistors in Series All resistors in series have the

same current (I)

Since Veq is the sum of all the individual V, Req must be the sum of all of the individual R:

Req = R1 + R2 + R3 …

Resistors in series addVeq

R1 R2

I

Resistors in Parallel

All resistors in parallel have the same V

Since the current through each is I = V/R and Ieq = V/Req:

1/Req = 1/R1 + 1/R2 + 1/R3 ...

V

R1

R2

Ieq

I1

I2

Next Time

Read: 19.1-19.4, 18.6, 19.7 Homework: Ch 18, P 7, 35, Ch 19,

P 5, 9