A circuit is constructed using the following materials: an ideal battery, a switch, an uncharged capacitor, and n = 3 resistors. The battery, switch, and capacitor are all connected in series. with each other (in that order); then the resistors are all con- nected in parallel to each other, and then placed between the capacitor and the battery. The battery has emf & = 12.0 V, the capacitor has capacitance C = 490 μF, and each resistor has resistance R = 320 kn. At t = 0, the switch is closed. How much energy E does the capacitor store when t 1.0 min? For the limit check, investigate what happens to E as the number. of parallel resistors gets large (n → ∞). = Initial Equations Algebra Work (Symbols only. Don't plug in any numbers yet.) Symbolic Answer: Unit Check Limit Check a) As n∞, what limit does E approach? b) Why does the result make physical sense? Numerical Answer: (Obtain this by plugging numbers into your symbolic answer.)

48 V + #F 68 ΚΩ www Ic + 20 www. 0 0000 1 22 ΚΩ = 10 nF 12 V Assume the capacitor to be fully discharged before the switch closes to position 1 at t=0: D. Determine equations for Ic(t) and Vc(t) in position 1. After a long time (i.e. >5 T, capacitor fully charged) the switch is moved to position 2: E. Determine equations for Ic(t) and Vc(t) in position 2. F. Provide a sketch of Ic(t) and Vc(t) for both cycles. Please label accordingly. F Vc

A 15 μF capacitor initially charged to 25 μC is discharged through a 1.2 kΩ resistor. How long does it take to reduce the capacitor's charge to 10 μC?

Bacteria and other prokaryotes are found deep underground, in water, and in the air. One micron (10-6 m) is a typical length scale associated with these microbes. (a) Estimate the total number of bacteria and other prokaryotes onthe Earth. (b) Estimate the total mass of all such microbes.

In the figure 1 = 4.38 V, 2 = 1.17 V, R₁ = 3.972, R₂ = 1.90 S2, R3 = 4.782, and both batteries are ideal. What is the rate at which energy is dissipated in (a) R₁, (b) R2, and (c) R3? What is the power of (d) battery 1 and (e) battery 2? ww R₁ www R₂ - 18₁ R$ Ef (a) Number i ! Units (b) Number Units (c) Number i Units (d) Number i ! Units (e) Number i ! Units ! [|]]] W W W W W

In the following circuit, lo = 0.171 A, I, = 0.043 A, and I2 = 0.129 A. Find the potential difference from A to B going along the following paths (show all work): a) Through the battery and the 20 Q resistor on the bottom. b) Through the resistors in the middle (40 Q and 20 Q). c) Through the 20 Q resistor on the far right. A 40 O 6V 20 Ω 20 2 20 2 MacBook Pro B.

In the circuit in the following figure the two capacitors are initially charged at 45.0 V. (a) How long after closing the S switch the potential through each capacitor will be reduced to 10.0 V? (b) At that time, what will be the value of the current?

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A 10 kΩ resistor and a 3 nF capacitor are connected across a 10 V battery. The time it takes for the potential across the capacitor to reach 4 V is (a)   17.5 msecs (b)   15.3 msecs (c)   12.0 msecs (d)   18.0 msecs (e)   2.85 msecs

An initially uncharged parallel plate capacitor is connected to a circuit containing a battery with emf 8-42V and a resistor, R = 4.9MQ as shown in the figure to below. The capacitor whose plates have an area of A = 7.1mm² are separated by a distance of d = 5mm and one third of the capacitor is filled with a dielectric material, K₁ = 3.5 and the rest (two thirds) is filled with another dielectric material, K₂ = 3.4. At t=0 the switch is closed. 5.4 seconds after the switch is closed the electric field within the first dielectric material (K₁) is observed to be 18 × 106 N/C. Find the charge on the capacitor at this instant (t = 5.4s) in terms of permitivity of free space €0? Express your answer using zero decimal place. R E Answer: S K1 K2