1. DC circuits
Physics 114
11/23/2018
Lecture VI

2. 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.
11/23/2018
Lecture VI

3. 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.
11/23/2018
Lecture VI

4. Electric battery For idealized battery emf – supplied voltage
Real life batteries have internal resistance r
Terminal voltage (supplied to the circuit)
Vab=emf-Ir
11/23/2018
Lecture VI

5. Series vs parallel - Req
R1=R2R R2=R3=R
Req=3R4R
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.
11/23/2018
Lecture VI

6. Series vs parallel - I R1=R2R R2=R3=R Req=3R4R I=V/Req=V/3RV/4R
I1=I2=I3=I
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
11/23/2018
Lecture VI

7. 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 -
11/23/2018
Lecture VI

8. 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 -
11/23/2018
Lecture VI

9. Capacitor connections
No DC current
through capacitor,
Just store charge.
Parallel connection:
Same voltage – V1=V2=V3=V
Different charges:
Q1=C1V Q2=C2V Q3=C3V
Q=Q1+Q2+Q3=V(C1+C2+C3)
Ceq=C1+C2+C3
Series connection:
Same charge (QA=0  -Q1+Q2=0)
Different voltages V=V1+V2+V3
11/23/2018
Lecture VI

10. Safety and grounding Voltage does not kill. Current kills
1mA – “feel”
10mA – muscle contraction
70 mA – “ventricular fibrillation”
~1A – hearts stops (not as harmful)
>10A – “fry”
Usually V is fixed
To reduce I – increase R
Dry surface
Insulating sole
Insulating floor
To avoid high V -
Ground the case (3prong plug)
11/23/2018
Lecture VI