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Ohm’s Law
Physics 102
Professor Lee Carkner
Lecture 13
Circuit Theory
Potential difference (DV or V):

in volts (joules per coulomb)
Current (I):

I = DQ/Dt
in amperes (amps, coulombs per second)
Resistance (R):
how hard it is to get current to flow

in ohms (volts per ampere)
Resistance

Good conductors have low resistivity, good
insulators have high resitivities

The total resistance of the material also depends on
its size

The resistance can be written as:
R = r (L/A)
where r is the resistivity, L is the length, and A is the
cross sectional area
How much current do you
get if you put a potential
difference V across a wire
with resistance R?
High voltage, low resistance
means large current

Commonly written as:
V = IR
Every individual piece of a
circuit has its own value of V,
I and R and obeys Ohm’s law
Ohm’s Law
Temperature and Resistance
Resistors convert energy from the current
into heat

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
As current flows though a resistor, its resistance
changes (we usually neglect this)
Energy in Electric Circuits
Charges have energy:
converted to
converted to
Power radiated by resistor is:
(Energy/Coulomb)(Coulomb/Second) =
(Energy/Second)
IDV = P
Using Ohm’s law (DV = IR) we can write:
P = I2R and P = (DV)2/R
Lightbulbs
A common circuit element is the lightbulb

Household lightbulbs are rated in watts

Brightness of lightbulb = power
In the US, most power outlets produce 120
volts of potential difference

Those that do not use a transformer
Conservation of Charge
We can find V, R and I for different parts of
circuit by applying two conservation rules
(for charge and energy)

If the current splits, the two new currents
must sum to be equal to the original
Otherwise charge would be gained or lost
Conservation of Energy
Each resistor has a DV 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 DV
Since the change in potential energy is the same
for each
Resistors in Series
R1
R2
I
DVeq
All resistors in series have the same
current (I)

Since DVeq is the sum of all the
individual DV, Req must be the sum
of all of the individual R:
DVeq = IReq = IR1 +IR2
Req = R1 + R2 + R3 …

Note that the voltages add as well
Resistors in Parallel
R1
I1
Ieq
All resistors in parallel have the
same DV

R2
I2
DV
Since the current through each is I =
DV/R and Ieq = DV/Req:
DV/Req = DV/R1 + DV/R2
1/Req = 1/R1 + 1/R2 + 1/R3 ...

Next Time
Read: 19.1-19.4, 18.6, 19.7
Homework: Ch 18, P 7, 35, Ch 19, P 5, 9