Kirchhoff’s voltage law (KVL) Voltage (potential difference): total work per unit charge associated with the motion of charge between two points. 1 volt (V) = 1 joule (J) / coulomb (C) Potential energy: qV, produced by electric field mgh, produced by gravitation field

Kirchhoff’s voltage law (KVL): Cont. The sum of voltages around a closed loop is zero. -v1 + v2 = 0 + - Potential different (V) vs. potential (V) Potential: at each node, va, vb Potential difference: v2=va-vb Ground: true ground (earth) chassis ground (enclosure)

Circuit Elements and Their i-v Characterisitcs Resistance and Ohm’s Law: Resistance (R) depends on materials and geometry, and resistivity (r) only depends on materials.

Electric Power Electric power: moving charge  doing work (energy) Power (P) = Work / time = work / charge x charge / time = V I P = Joules / sec = Watts (W) What are paying for electricity bill ? kW H = energy

More on Resistance Home electric appliances: what does a 1000 W hair dryer tell you? Always assume 120V if the voltage is not specified. Never exceed the rated power. Can you use these appliances in 220 V lines. You destroy the appliance! You can use appliances rated with 220V in 110 V, but with much lower power than rated. (Exercise)

Open and Short Circuits Short Circuit: R=0, v=0 for any i. Particularly bad for voltage source. Open Circuit: R  ∞, i=0 for any v. Particularly bad for current source.

Series Resistors and the Voltage Divider Rule Series Circuit: One branch  same current through each resistor. Voltage Divider:

Example: voltage divider If you want to use your car battery (12 V) to power your laptop computer which requires 3V power supplier, how would you do it.

Parallel Resistors and the Current Divider Rule Parallel Circuit: resistors share the same terminal  same voltage on each resistor. Current Divider: Large current though smaller R Advantage of parallel circuit: a broken branch will not affect other branches