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

Last Time This One Capacitors Resistors Physical C = e0A/d Series 1/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

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

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

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=1/2QV 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!

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

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

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: I1 + I2 = Ieq Voltage is same across each: V1 = V2 = Veq Req R1 R2

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

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!!