Assignment #7

Section 25-1, 25-2, & 25-3

Date Due: Mon. Oct. 13

7-1. A parallel plate capacitor has an area of 47.0 cm² {5.00 cm²} and a separation of 1.26 mm.

(A) What is the capacitance of this capacitor in picofarads? Ans:{3.51 pF}

(B) What voltage would be needed to transfer 5.50 nanocoulombs {19.0 nC} of charge to the plates of this capacitor? Ans:{5.41 kV}

(C) If voltage between the two plates is adjusted until the electric field between the two plates is 780 kV/m, what is the charge stored on either plate? Ans:{3.45 nC}

7-2. A spherical capacitor has an outer surface area of 47.0 cm² {5.00 cm²} and a 1.50 mm separation between the outer and inner spherical surfaces.

(A) What is the capacitance of this arraignment? Ans:{2.25 pF}

(B) How much energy is stored in this capacitor if 170 mC is placed on the outer surface? Ans:{6.42 kJ}

Assignment #8

Section 35-4 & 25-5

Date Due: Tue. Oct. 14

Capacitor Circuits

8. The three capacitors C₁, C₂, and C₃ have capacitances of 4.90, 1.60, and 8.50 microfarads each {3.50, 2.70, and 6.60 mF}. A 9.00 Volt battery is connected across the combination.

(A) What is the equivalent capacitance C_e of a single capacitor that has the same capacitance as the combination of all three capacitors in this arrangement? Ans:{C_e = 5.42 mF}

(B) What is the charge stored on capacitor C₁?

(C) What is the voltage across capacitor C₂? Ans:{V₂ = 6.39 V}

(D) How much energy is stored in capacitor C₃? Ans:{U₃ = 22.5 mJ}

BONUS:

(E) If Mica with a dielectric constant of k = 5.40 is inserted into capacitor C₂ only, what is the charge across capacitor C₃? Ans:{ Q₃ = 40.9 mC}

9. A 1.20 km {78.0 m} length of 10 gauge wire (diameter = 2.588 mm) is made of Aluminum (r = 2.70 g/cm³, M = 26.98 gm/mole, r = 2.82x10^-8 W m) {Silver (r = 10.5 g/cm³, M = 107.9 gm/mole, r = 1.59x10^-8 W m}. The end of the wire is connected across a 12.0 volt battery.

(A) What is the resistance of the wire in ohms and the current flowing through the wire? Ans:{R = 0.237 W, I = 50.6 Amps}

(B) How many electrons flow through the wire in 2.90 minutes? Ans:{5.49x10²² electrons}See Current and Drift Velocity

(C) What is the expected electron density of the conduction electrons if every atom in the wire contributes one electron to the current flow and the current flow is uniform across the interior of the wire? Ans:{r _n = 5.86x10²⁸ electrons/m ³}

(D) How long does it take for a conduction electron to travel the length of the wire? Ans:{21.2 hr}

(E) What is the electric field in the wire? Ans:{0.154 N/C}

(F) How many watts of energy will be converted into heat due to the resistance of the wire to the flow of conduction electrons? Ans:{607 W}

Assignment #10

Section 26-4

Date Due: Fri. Oct. 17

DC Circuits

10. Four resistors R₁, R₂, R₃, & R₄ have resistances of 14.0 W, 8.80 W, 12.0 W, & 7.70 W { 330 W, 1460 W, 2500 W, & 990 W}. A 12.0 V {45.0 V} battery with no internal resistance is connected to the combination shown.

(A) What is the equivalent resistance of the combination of all four resistors? Ans:{2,240 W}

(B) What is the current through and the voltage drop across resistor R₁? Ans:{20.1 mA, 6.62 V}

(C) What is the current through and the voltage drop across resistor R₃? Ans:{7.40 mA, 18.5 V}

(D) What is the power dissipated by resistor R₄? Ans:{399 mW}

BONUS:

(E) If the battery has an internal resistance of .550 W {19.0 W}, how much heat will the battery dissipated in 3.50 minutes? Ans:{1.58 J}

Assignment #11

Section 26-5

Date Due: Mon. Oct. 20

Complex DC Circuits

11. The three resistors R₁, R₂,& R₃ have resistances of 22.0 kW, 9.90 kW, & 11.0 kW {380 W, 590 W, & 790 W}. The two batteries have emf's of 29.0 V and 14.0 V with no internal resistance.

(A-C) Determine the magnitude and direction of the current through each of the resistors? Ans:{ I₁ = 32.1 mA A to B, I₂ = 28.5 mA B to D, I₃ = 3.56 mA C to D}

(D) What is the voltage drop between points A & C and B & D? Ans:{ V_AC = 26.2 V, V_BD = 16.8 V}

BONUS:

(E) If the 14.0 V battery is replaced with by a new battery, what value of the emf V₂ for the second battery would produce no current through resistor R₁? Ans:{ V₂ = 67.8 V}

Assignment #12

Section 26-6

Date Due: Tue. Oct. 21

RC Circuits

12. A 12.5 mF {6.50 mF} capacitor is connected in series to two parallel resistors R₁ = 13.0 W and R₂ = 18.0 W and one series resistor R₃ = 8.50 W as shown. The combination is connected to a 9.50 V {24.0 V} battery with no internal resistance. The capacitor is initially uncharged.

(A) When the battery is first connected, what is the current through resistor R₁ and the voltage drop across the capacitor? Ans:{868 mA,? V}

(B) What is the time constant of this circuit? Ans:{104 ms}

(C) What is the voltage across resistor R₁, and the charge stored in the capacitor, 35.0 ms after the battery is connected? Ans:{ V_R1 = 8.07 V, Q = 44.5 mC}

(D) How long will it take for 600 trillion electrons to be stored in the capacitor after the capacitor is connected? Ans:{99.9 ms}

BONUS:

(E) At what moment after the battery is connected will the voltage across resistor R₃ equal the voltage across the capacitor? Ans:{ 44.3 ms}

Assignment #14

Review

Date Due: Wed. Oct. 22

14-1. A battery with an emf of 18.0 V and negligible internal resistance is connected to a circuit consisting of two series resistors and two series capacitors connected in parallel as shown.

When the switch is open, what are the steady state values of the

(A) current through the resistors? Ans:{500 mA}

(B) charge on the capacitors? Ans:{75.6 mC}

(C) potential (relative to ground) at the points a, b, c, & d? Ans:{18 V, 12.5 V, 5.81 V, 0}

When the switch is closed, what are the steady state values of the

(D) potential at points b and c? Ans:{V_b = V_c = 12.5 V}

(E) charge on the capacitors? Ans:{34.1 mC, 163 mC}

BONUS:

(F) How many coulombs of charge flows through the switch when the switch is first closed? (Hint, look at the charge on capacitors before the switch is closed and after it is closed.)