DC Circuits Currents. Resistors. Batteries. Kirchhoff’s Loop Rules. Power.
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Transcript of DC Circuits Currents. Resistors. Batteries. Kirchhoff’s Loop Rules. Power.
DC Circuits
Currents. Resistors. Batteries.
Kirchhoff’s Loop Rules. Power
Examples of Circuits
t
QI
av
Current: flow of charge
Average current: Iav= Charge Q
flowing across area A in time t
t
QI
d
d
Instantaneous current: differential limit of Iav
Units of current: Coulomb/second=Ampere (A)
Direction of the current
Direction of current is in direction of flow of positive charge
or, opposite direction of flow of negative charge
Current density J (1)J: current/unit area
A
IJ
points in the direction of the current
Units A/m2
J
Current density J (2)If the ara is not perpendicular to the current
An area or surface perpendicular to the direction of the current
)cos(n JAJAI
: angle between normal to A and current
nA
IJ
)cos(n AA
Why does current flow?If an electric field is set up in a conductor, charge will move (making a current in the direction of E)
Note that when current is flowing, the conductor is not an equipotential surface (and Einside0)!
Microscopic picture (1)
Drift speed is velocity forced by applied electric field in the presence of collisions, it is typically 4x10-5m/s, or 0.04 mm/s!
To go one meter at this speed takes about 10 hours
Thermal velocity is around 103 km/s !
How can this be?
Microscopic picture (2)
vd : drift velocity
n : number of carriers per unit volume
q : charge of each carrier (normally e)
A : suface perpendicular to vd
AqnvI d
dqnvJ
Conductivity and resistiviy
Ability of current to flow depends on density of charges & rate of scattering.
Two quantities summarize this:
: conductivity
: resistivity 1
Microscopic Ohm’s Law
And depend only on the microscopic properties of the material,
not on its shape
1
or JEEJ
The voltage drops in a resistorThe electric field brings about a voltage drop in a resistor
ElVVV ab
What is the relationship between V and current?
ElVVV ab
Ohm’s Law (1)
A
lIl
A
IJlElV
R has units of ohms ()=Volt/Amp
Ohm’s Law (2)
A
lR IRV
Then, units of : m and : -1m-1
Examples of Circuits
Symbols for circuit elements
Electromotive force -Battery Moving from the negative to positive terminal of a battery increases your potential
Think:
Ski Lift
ab VVV
Internal resistanceReal batteries have an internal resistance, r, which is small but non-zero
IrVVV ab Terminal voltage:
Real battery=ideal battery in series with a resistance
Sign conventions - ResistorMoving across a resistor in the direction of current decreases your potential
ab VV Think:
Ski Slope
Voltage drop:
Voltage decreases in the direction of the current
Sign conventions - CapacitorMoving across a capacitor from the negatively to positively charged plate increases your potential
ab VVV
Resistors in seriesThe same current I must flow through both resistors
eq2121 )( IRRRIIRIRVVV ca
21eq RRR
N
iiRR
1eq
or
Resistors in parallelVoltage drop across the resistors must be the same
eq221121 IRRIRIVVV
N
i iRR 1eq
11
eq212121
11
R
V
RRV
R
V
R
VIII
21eq
111
RRR or
Measuring V, I, R
Measuring Potential Difference A voltmeter must be hooked in parallel across the element you want to measure the potential difference across
Voltmeters have a very large resistance, so that they don’t affect the circuit too much
Measuring CurrentAn ammeter must be hooked in series with the element you want to measure the current through
Ammeters have a very low resistance, so that they don’t affect the circuit too much
Measuring ResistanceAn ohmmeter must be hooked in parallel across the element you want to measure the resistance of
Here we are measuring R1
Ohmmeters apply a voltage and measure the current that flows. They typically won’t work if the resistor is powered (connected to a battery)