Physics 1161 PreLecture 06 Circuits and Ohms Law

Physics 1161: Pre-Lecture 06 Circuits and Ohm’s Law • textbook sections 21 -1 -- 21 -4 Homework, keep lots of digits!

Last Time • Capacitors – Physical – Series – Parallel – Energy • Resistors – Physical – Series – Parallel – Power C = e 0 A/d 1/Ceq = 1/C 1 + 1/C 2 Ceq = C 1 + C 2 U = 1/2 QV This One R = r L/A Req = R 1 + R 2 1/Req = 1/R 1 + 1/R 2 P = IV

Electric Terminology • Current: Moving Charges – 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

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 L • Ohms Law I = V/R – Double potential difference double current A

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

Comparison: Capacitors vs. Resistors • Capacitors store energy as separated charge: U=1/2 QV – Capacitance: ability to store separated charge: C = ke 0 A/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!

Resistors in Series • One wire: – Effectively adding lengths: R – Since R L, add resistance: Req = R 1 + R 2 = R 2 R

Resistors in Series • Resistors connected end-to-end: – If current goes through one resistor, it must go through other. I 1 = I 2 = Ieq – Both have voltage drops: V 1 + V 2 = Veq R 1 Req R 2

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

Resistors in Parallel • Both ends of resistor are connected: – Current is split between two wires: I 1 + I 2 = Ieq – Voltage is same across each: V 1 = V 2 = Veq R 1 R 2 Req

Summary Series Parallel R 1 R 2 Wiring Each resistor on the same wire. Each resistor on a different wire. Voltage Different for each resistor. Vtotal = V 1 + V 2 Same for each resistor. Vtotal = V 1 = V 2 Current Same for each resistor Itotal = I 1 = I 2 Different for each resistor Itotal = I 1 + I 2 Increases Req = R 1 + R 2 Decreases 1/Req = 1/R 1 + 1/R 2 Resistance

Parallel + Series Tests • Resistors R 1 and R 2 are in series if and only if every loop that contains R 1 also contains R 2 • Resistors R 1 and R 2 are in parallel if and only if you can make a loop that has ONLY R 1 and R 2 • Same rules apply to capacitors!!