DC circuits
Physics 114
7/24/2016
Lecture VI
1
Test problem
• For resistors connected in series, which of the
following will be the same for each of the
resistors?
• A
The current through.
• B
The potential difference across.
• C
The resistance of.
• D
The power dissipated by.
7/24/2016
Lecture VI
2
Test problem
• For resistors connected in parallel, which of the
following will be the same for each of the
resistors?
• A
The current through.
• B
The potential difference across.
• C
The resistance of.
• D
The power dissipated by.
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Lecture VI
3
Electric battery
•
•
•
•
For idealized battery emf – supplied voltage
Real life batteries have internal resistance r
Terminal voltage (supplied to the circuit)
Vab=emf-Ir
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Lecture VI
4
Series vs parallel - Req
• R1=R2R
• Req=3R4R
R2=R3=R
• R1=R2R
R2=R3=R
• Req=R/3=2R/62R/5
If any of R’s increased the equivalent resistance will increase
in both parallel and series connection.
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Lecture VI
5
Series vs parallel - I
•
•
•
•
R1=R2R
R2=R3=R
Req=3R4R
I=V/Req=V/3RV/4R
I1=I2=I3=I
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•
•
•
•
•
Lecture VI
R1=R2R
R2=R3=R
Req=R/3=2R/62R/5
I=V/Req=6V/2R5V/2R
I1=V/R1=V/RV/2R
I2=I3=V/R – the same
6
Kirchhoff’s rules
• Junction rule (charge conservation):
– At any junction point the sum of all current entering the
junction must equal the sum of all currents leaving the
junction
• Do not disregard signs!
• Assign initial signs based on your best guess – if you were wrong the
currents will turn to be negative (opposite to initial guess)
• Loop rule (energy conservation):
– The sum of the changes in potential around any closed path of
a circuit must be zero.
•
•
•
•
•
Choose a direction in which you circle the loop (random)
For resistor Vab=-IR – negative if current along the loop direction
For resistor Vab=+IR – positive if current opposite the loop direction
For battery Vab – positive if the direction is from – to +
For resistor Vab –negative if the direction is from + to -
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Lecture VI
7
Kirchhoff’s rules
• Loop rule (energy conservation):
– The sum of the changes in potential around any closed path of
a circuit must be zero.
•
•
•
•
•
Choose a direction in which you circle the loop (random)
For resistor Vab=-IR – negative if current along the loop direction
For resistor Vab=+IR – positive if current opposite the loop direction
For battery Vab – positive if the direction is from – to +
For resistor Vab –negative if the direction is from + to -
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Lecture VI
8
Capacitor connections
No DC current
through capacitor,
Just store charge.
• Parallel connection:
• Series connection:
• Same voltage – V1=V2=V3=V • Same charge (QA=0  -Q1+Q2=0)
• Different charges:
• Different voltages V=V1+V2+V3
– Q1=C1V Q2=C2V
Q
Q Q Q
 

Q3=C3V
Ceq C1 C2 C3
– Q=Q1+Q2+Q3=V(C1+C2+C3)
1
1
1
1
 

– Ceq=C1+C2+C3
Ceq C1 C2 C3
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Lecture VI
9
Safety and grounding
• Voltage does not kill.
• Current kills
• Usually V is fixed
• To reduce I – increase R
• Dry surface
– 1mA – “feel”
• Insulating sole
– 10mA – muscle contraction
• Insulating floor
– 70 mA – “ventricular fibrillation”
– ~1A – hearts stops (not as harmful)• To avoid high V • Ground the case
– >10A – “fry”
(3prong plug) 10
7/24/2016
Lecture VI