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