Battery or “power supply” Boosts the potential energy of charges that pass through it. Compare to a water pump Current Unit ampere: 1 A = 1 C/s Because I is in the direction of + charges, it’s easier to just imagine + charges moving in circuits

Resistance Describes how hard it is for current to flow through an object Unit ohms: This is Ohm’s law: The voltage needed to cause a current I is proportional to R:

P1. A cylindrical resistor is 4 ohms P1. A cylindrical resistor is 4 ohms. A second resistor is made of the same material, but is twice as long and twice the diameter, so it has a resistance of ___________ ohms A. 1 B. 2 C. 4 D. 8 E. 16

Power in circuits We shorten DV to V

Capacitor Two conductors meant to hold energy in separated equal charges +Q and –Q. To separate the charges requires work, so there is a potential (voltage) difference V between the two. Capacitance measures how much charge a capacitor separates (“holds”), per volt potential difference. units: 1 Farad = 1 coul/volt

Capacitor Uses keyboard keys: the plates don’t have to touch to sense movements touchscreens and touch switches (some lamps) used to smooth fluctuations in circuits, power supplies used to store energy for large pulses of current (tasers, defibrilators)

Energy stored in capacitor Analogy: What is the potential energy of a total mass M of boxes stacked on top of each other to a height h above the ground? Demo: 9mF capacitor charged to 100 V:   Ecap = 45 J This much energy would throw a tennis ball (60g) to a height of 80 m!  

Contrast these uses of q, Q and V General equation of PE of any charge at a spot that has voltage V Only used for the total energy of a capacitor charged to Q,V

Parallel plate capacitor Permittivity of free space is the dielectric constant of the material between the plates (k =1 for vacuum, air ). C depends only on conductor dimensions and the material in the space between the conductors, not on Q or V. If we double Q, V doubles, but C stays the same.

Capacitors in series or parallel For capacitors in parallel ______ is the same For capacitors in series ______ is the same

Mixed series and parallel At each step, combine any C’s obviously in series or parallel, and draw a new circuit

P2. If each capacitors is 2F, the total capacitance is closest to ___ F A. 0.8 B. 1.2 C. 4.0 D. 6.0 E. 8.0 + V -  

Finding Q and V for each capacitor Work backwards from the final Ctot. From the battery voltage find Qthrough_battery for Ctot. The outermost plates connected to the battery have Qthrough_battery on them, because that much charge went through the battery. The sum of all the DV’s must add up to battery voltage for any path through the capacitors Any piece of connected conducting plates+wire must have net zero charge. Parallel: same DV. Series: same Q

Find Q, V for each capacitor, if we connect these to an 8V battery. If we don’t finish it, see class notes link on Max for complete solution.

P3. If each capacitors is 2F, and Vbattery = 10 V, the charge on capacitor A is closest to__C 2.0 4.0 6.0 8.0 10.0 + V -   D A B C Leyden Jar demo