Dc Circuit
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Transcript of Dc Circuit
DC CircuitsDC Circuits
The circuitThe circuitResistance in combinationsResistance in combinations
Kirchhoff’s RulesKirchhoff’s RulesRC transient circuitsRC transient circuits
dq
dWε
Work done by a battery on charge
Here AB εε
Real Battery and Single Loop circuits… What’s the current ?Real Battery and Single Loop circuits… What’s the current ?
Conservation of energy: Kirchoff’s first Law: Sum of voltages in a closed loop is zero.
2)( Rr
R
RiP
Rri
0iRir
ViRirV
2
2
R
aa
Real Circuit with ammeter and voltmeter
Equivalent ResistanceEquivalent ResistanceResistors in SeriesResistors in Series
Series requirementsSeries requirements– Conservation of energyConservation of energy– Potential differences addPotential differences add– Current is constantCurrent is constant
n21 VVVV ...Apply Ohm’s Law to each resistorApply Ohm’s Law to each resistor
n21eq IRIRIRIR ...
n21eq RRRR ...
Resistors in parallelResistors in parallel
Parallel requirementsParallel requirements– Charge conservationCharge conservation– Currents must addCurrents must add– Potential difference is Potential difference is
same across each resistorsame across each resistor
321 iiii
Apply Ohm’s Law to each resistorApply Ohm’s Law to each resistor
n21eq RV
RV
RV
RV
...n21eq R1
R1
R1
R1
...
Example 1
What is current through battery?
What is current through i2 ?
Kirchhoff’s RulesKirchhoff’s Rules1 The algebraic sum of the currents The algebraic sum of the currents
entering a junction is zero.entering a junction is zero. ((ConservationConservation of Charge of Charge))
2 The algebraic sum of the changes in The algebraic sum of the changes in electric potential difference around electric potential difference around any closed circuit loop is zero.any closed circuit loop is zero. ((Conservation of EnergyConservation of Energy))
Signs for Rule 2Signs for Rule 2The direction of travel when traversing The direction of travel when traversing the loop is from a to b.the loop is from a to b.
Problem 2
Find the currents in each of the three legs of the circuit,
321 i,i,i
Three unknowns, need three equations. Also since batteries are in there cannot reduce the resistances since none in parallel or series
Example: Applying Kirchhoff’s RulesExample: Applying Kirchhoff’s Rules
Apply Kirchhoff’s first rule to Apply Kirchhoff’s first rule to the three wire junction at the three wire junction at the bottom of the diagramthe bottom of the diagram
0III 312
Apply Kirchhoff’s second Apply Kirchhoff’s second rule to the closed path in red, rule to the closed path in red, traversing it clockwisetraversing it clockwise
0I05I03V05 21 ...
Apply Kirchhoff’s second rule Apply Kirchhoff’s second rule to the closed path in green, to the closed path in green, traversing it clockwisetraversing it clockwiseNote the sign changes for Note the sign changes for some of the elementssome of the elements
0I07V010I03V05 31 ....
Another, example: applying Kirchhoff’s RulesAnother, example: applying Kirchhoff’s Rules
Solve the equations Solve the equations simultaneously for the values simultaneously for the values if I. If I is negative the if I. If I is negative the current is in the opposite current is in the opposite directiondirection
0III 312
0I05I03V05 21 ...
0I07I03V05 31 ...
A7740I
A9150I
A1410I
3
2
1
.
.
.
RC Circuits and Time dependenceRC Circuits and Time dependenceTime dependence
Recall Lab 7! Resistor slows down the charging
of the capacitor
Time dependent behavior Time dependent behavior (transient) 2 cases: switch at (transient) 2 cases: switch at
““a” or at “b”a” or at “b”
a)a) ChargingChargingb)b) dischargingdischarging
In position “a” Charging the In position “a” Charging the CapacitorCapacitor
Use Kirchhoff’s Loop ruleUse Kirchhoff’s Loop rule
RCt
c
RCt
R
e1V
e1Cq
RRC
q
dt
dq
0IRq
0VV
(t)
(t)
(t)(t)
C-
- c
Or the voltage across capacitor is …..
What’s VR across resistor?Find the current and multiply by R
,or ....
get and derivative take
(t)
(t)
(t)(t)
(t)
RCt
R
RCt
RCt
e
Rdt
dqV
eR
I
dt
dqI
e1Cq
RCt
0c
RCt
0
RCt
0
R
eVV
eCVeqq
RC
q
dt
dq
0VV
(t)
(t)
(t)(t)
c
Discharging Position b:
1. Charging the Capacitor1. Charging the Capacitor
Note:Note: RCis called the time constantis called the time constantWhat are the units?What are the units?