1. Circuits and Ohm’s Law Physics 1161: Pre-Lecture 08
textbook sections
Homework, keep lots of digits! 1

2. Last Time This One Capacitors Resistors Physical C = e0A/d
Series /Ceq = 1/C1 + 1/C2
Parallel Ceq = C1 + C2
Energy U = 1/2 QV
This One
Resistors
Physical R = r L/A
Series Req = R1 + R2
Parallel 1/Req = 1/R1 + 1/R2
Power P = IV

3. Electric Terminology Current: Moving Charges Power: Energy/Time
Symbol: I
Unit: Amp  Coulomb/second
Count number of charges which pass point/sec
Power: Energy/Time
Symbol: P
Unit: Watt  Joule/second = Volt Coulomb/sec
P = IV

4. Physical Resistor
Resistance: Traveling through a resistor, electrons bump into things which slows them down. R = r L /A
r: resistivity; constant that depends on the material (i.e. copper, silver, aluminum, etc.)
L: length of the wire
A: cross sectional area of the wire
Ohms Law I = V/R
Double potential difference  double current A L

5. Resistivity:  Material Resistivity at 20°C Ω·m µΩ·cm silver
1.6 × 10-8
1.6
copper
1.7 × 10-8
1.7
gold
2.2 × 10-8
2.2
aluminium
2.7 × 10-8
2.7
magnesium
4.2 × 10-8
4.2
tungsten
5.4 × 10-8
5.4
nickel
6.9 × 10-8
6.9
iron
10.1 × 10-8
10.1

6. Comparison: Capacitors vs. Resistors
Capacitors store energy as separated charge: U=1/2QV
Capacitance: ability to store separated charge: C = ke0A/d
Voltage determines charge: V=Q/C
Resistors dissipate energy as power: P=VI
Resistance: how difficult it is for charges to get through: R = r L /A
Voltage determines current: V=IR
Don’t mix capacitor and resistor equations!

7. Resistors in Series = One wire: Req = R1 + R2
Effectively adding lengths:
Since R  L, add resistance: R R
Req = R1 + R2

8. Resistors in Series Resistors connected end-to-end: I1 = I2 = Ieq
If current goes through one resistor, it must go through other.
I1 = I2 = Ieq
Both have voltage drops:
V1 + V2 = Veq R1
Req R2

9. Resistors in Parallel = Two wires: Effectively adding the Area
Since R a 1/A add 1/R: = R R
R/2

10. Resistors in Parallel Both ends of resistor are connected:
Current is split between two wires:
I1 + I2 = Ieq
Voltage is same across each:
V1 = V2 = Veq
Req R1 R2

11. Summary Series Parallel Wiring Voltage Current Resistance R1 R1 R2 R2
Each resistor on the same wire.
Each resistor on a different wire.
Wiring
Different for each resistor.
Vtotal = V1 + V2
Same for each resistor.
Vtotal = V1 = V2
Voltage
Same for each resistor
Itotal = I1 = I2
Different for each resistor
Itotal = I1 + I2
Current
Increases
Req = R1 + R2
Decreases
1/Req = 1/R1 + 1/R2
Resistance

12. Parallel + Series Tests
Resistors R1 and R2 are in series if and only if every loop that contains R1 also contains R2
Resistors R1 and R2 are in parallel if and only if you can make a loop that has ONLY R1 and R2
Same rules apply to capacitors!!