Test 4 Aut. 2001, Monday Lecture-Click here for the Tues-lec test. |
1. (36 points) A voltage of exactly V = 4000 Volts is aplied across the cylindrical plates of a capacitor of length L = 0.0200 m = 2.00 cm. Note: Inner radius =a = 0.00060 m = 0.0600 cm and outer radius= b = 0.00120 m = 0.12 cm. Note that the scale used in the diagram may not reflect these dimensions.
(a) (20 points) What is the charge per unit length (in C/m) on the inner cylindrical shell of radius a ?
(b) (10 points) What is the magnitude E of the electric field at a distance r = 0.00100 m from the central axis of the capacitor?
(c) (6 points) Suppose the energy in the capacitor is used to heat up a very small piece of metal of specific heat Cx = 128.0 J/kg 0C and mass
6.00 x10-10 kg. If the initial temperature of the metal is exactly 200 C, then what is the final temperature ? Assume heating only.
Solutions: (a) Q/4000 = L/[2k ln(b/a)] solve for Q/L = 3.21x10-7 C/m (b) E = (Q/L)/(2kr) = 5770000 N/C (c) CV2/2 = mC(Tf - Ti) so that Tf = 187 0C This prob. is tight ! |
2
. (30 points) A cylindrical resistor of outer diameter d = 0.000100 m = 0.0100 cm has a hole that runs along the axis. The cross-sectional shape of the hole is a square circumscribed by the outer circular border of the cylinder. The resistor has a length L = 0.300 m. See the diagram below. The resistivity of the material is 1.7x10-8 ohm-m. Suppose a battery of exactly V= 110 Volts is connected to the ends of the resistor. Suppose that the resistor is then submerged in a vat of water of mass m = 1.00 kg. How long does it take the resistor to heat up the water from exactly 10 oC to exactly 90 oC ? Cw = 4186 J/oC kg
Need this: AREA= CIRCLE AREA - SQUARE
AREA = |
3. Extra Credit. (8 points) The battery voltage = 10 Volts. Assume:
How long ( in seconds) does it take resistor R2 to generate 1000 Joules of heat ?
Solutions: 1/Rp
= 1/2 + 1/1 + 1/4 =
7/4 |