Physics 106 Lesson #12 Series & Parallel Circuits II Dr. Andrew Tomasch 2405 Randall Lab atomasch@umich.edu

Review: Series Resistors For resistors R1 & R2 connected in series (sequentially), the current i passing through each resistor must be the same The voltages across R1 & R2 must add up to V (Loop Rule) V +

Review: Parallel Resistors Resistors R1 & R2 connected in parallel have the same potential difference (voltage) V across them Charge must be conserved, so the currents I1 & I2 flowing through the two resistors must add up to the total current I leaving the battery (continuity for electric current!) Junction Rule V +

Review: Power Power has a precise definition in physics: Power is the rate at which work is done or how much work is done per unit of time Units: J/s  Watt (W) James Watt invented the steam engine In an electric circuit power is the product of current and voltage:

Concept Test #1 The circuit in front of you initially contains a single light bulb, bulb A, that burns with a certain brightness. We will now add an identical bulb, bulb B, in series with bulb A. What will happen? (Hint: brightness is determined by power and hence current.) Both will shine with the same brightness as bulb A did before. Both will shine with equal brightness, but they will be dimmer than before. Both will shine with equal brightness, but they will be brighter than before. Whether A or B is brighter depends on the direction of the current. A The total resistance in the circuit increases after adding light bulb B, so the current decreases. Because the light bulbs are in series, the current though each light bulb is the same. B

Concept Test #2 A B The circuit in front of you contains a single light bulb, bulb A, that burns with a certain brightness. We will now add an identical bulb, bulb B, in parallel with bulb A. What will happen? Both will shine with the same brightness as bulb A did before. Both will shine with equal brightness, but they will be dimmer than before. Both will shine with equal brightness, but they will be brighter than before. Whether A or B is brighter depends on the direction of the current. In parallel, bulb B is connected across the battery in exactly the same way as bulb A and will draw the same current as A, resulting in the same brightness as bulb A.

Kirchhoff's Rules A B Two simple rules which apply to any circuit: I1 = I2 + I3 + I4 Two simple rules which apply to any circuit: Junction rule: the total current into any point = total current out (what flows in must flow out…) Continuity for current! Loop rule: around any closed loop, increases in potential equal decreases in potential  the electric force is conservative no work done in a closed loop  you end up at the same potential (energy) as where you started (just like gravity)! Gustav Robert Kirchhoff A B Start and End Here