P2. Assume an ideal battery. When the switch is closed, what changes? A. Vbatt B. Ibatt C. Vbatt and Rtot D. Ibatt and Rtot

P7. When a third identical bulb (resistor) is added as shown, which changes? A. DVa B. DVb C. both D. neither P8. …so A. a is brighter, b is dimmer B. a is dimmer, b is brighter C. a is brighter, b is unchanged D. a is unchanged, b is dimmer E. a is unchanged, b is brighter

P8. When the wire near b is added in the corner, A P8. When the wire near b is added in the corner, A. a is brighter, b is dimmer B. a is dimmer, b is brighter. C. a is unchanged, b is dimmer. D. a is brighter, b is unchanged. E. both are unchanged

Kirchhoff’s Laws (we’ve used these ideas before) Sum of voltage changes around any loop is zero. DV is + if you move upstream, - if you move downstream Current into any junction must equal the current out of the junction. Some circuits (e.g. with batteries in different segments) we can’t simplify to one battery and one resistor Req. Use Kirchhoff’s rules to write equations and solve for unknowns.   Guess any direction for currents to start…if you’re wrong, that current will be opposite (negative) in the solution.

Kirchhoff’s Laws Goal: Find the three currents Write equations for as many loops (there are 3) and junctions as you need to find unknowns

Kirchhoff’s Laws become One way to start: substitute last into first: Put this into the second:

Kirchhoff’s Laws Now go back and check diagram with: Sum of voltage changes around any loop is zero Current into any junction must equal the current out of the junction.

P1. Which circuit puts out the most power? A. top B. bottom C. same

P2. When the wire is clipped on as shown how many bulbs get dimmer. A P2. When the wire is clipped on as shown how many bulbs get dimmer? A. 0 B. 1 C. 2 D. 3 E. 4 How many bulbs get brighter_____?

When the switch is closed, what happens?

P3. If the upper right bulb is removed, leaving an air gap, the current through the battery_____. A. increases B. decreases C. stays the same

P4. If the upper right bulb is removed, the voltage difference across the lower right bulb A. increases B. decreases C. stays the same

It takes time to discharge a capacitor The characterstic time is the “time constant” t = RC. Even if we don’t intentionally put a R or C in the circuit, each circuit has them.

It takes the same time to charge a capacitor Voltages around loop add to zero, so we can always find VR (and I) from VC

It takes time to charge a capacitor Right when the switch is closed, Q = 0, and VC = 0. So C acts like a ______. Long after the switch is closed, VC = Vbattery, and I is 0. So C act like a ______.

P5. Right after the switch is closed, which bulb is brightest. A P5. Right after the switch is closed, which bulb is brightest? A. Left B. Right C. the same P6. Long after the switch is closed, which bulb is brightest?

P7. After we close the switch, (before the C has charged much at all), the current through the battery is closest to _______ A. A. 1 B. 2 C. 3 D. 4 E. 5 P8. After we close the switch, and C is fully charged, the current through the battery is closest to _______ A. A. 0 B. 2 C. 3 D. 4 E. 5

Practice writing loop and junction equations to find unknowns.