PHYS 251 TEST #2 6/16/06 Dr. Holmes NAME
DO ALL EIGHT PROBLEMS. THE WORTH OF EACH PROBLEM IS MARKED BESIDE THE PROBLEM. SHOW YOUR WORK FOR PARTIAL CREDIT.
For problems 1d, 4d, 4e, and 5c, use one of the following answers:
a) increase by a factor of 4
b) increase by a factor of 2
c) increase by some factor OTHER THAN 2 or 4
d) stay the same
e) decrease by a factor of 1/2
f) decrease by a factor of 1/4
g) decrease by some factor OTHER THAN 1/2 or 1/4
h) can't determine whether it will change based on info given.
1) a) Through what potential difference should an electron be accelerated to reach a speed of 31 million (3.1x107) m/s if it starts from rest?
b) Should the final voltage be higher or lower than the initial voltage?
c) If a proton were to be accelerated by the same voltage, would it be going slower, the same speed, or faster than the electron?
d) If you doubled the voltage through which the electron of part a above was accelerated, would the final speed of the electron: (see answer selection above)
c (increase by some other factor: by 21/2).
For problem 2, consider the following situation: point C located at (0 m,
Particle A has qA = +7 mC located at (+6 m, 0 m); particle B has qB = -4 mC located at ( -2 m, 0 m).
2) a) Assuming that the voltage is zero at infinity, what is the voltage at the point C?
b) How much energy would it take to bring a third charge of +5 mC from very far away (assume infinitely far away) and place it at point C? [Note: a + answer indicates it takes energy to make the move, a negative answer indicates it gives up energy in the move.]
-2.97 x 10-3 Joules = -2.97 mJ.
3) DESIGN a 4.7 pF capacitor (that is, specify the 'geometry' and the materials to be used). Be sure to make a drawing showing all the values required by your design.
4) Consider a coaxial cable that has an inner wire of radius 2 mm and an outside cylinder of radius 11 mm. The cable is 3 m long. A voltage of 35 volts is placed across the inner wire and the outer cylinder. Assume that vacuum is between the wire and the cylinder.
a) What is the capacitance of the cable?
9.78 x 10-11 F = 97.8 pF.
b) What is the magnitude of the charge on the inner wire when the 35 volts is placed across the wire and cylinder?
3.42 x 10-9 Coul = 3.42 nCoul.
c) If the inner wire has the lower voltage, does it have the positive or negative charge on it?
d) If the voltage is doubled to 70 volts, how will the capacitance change (see page 1 for choices) ?
e) If the radius of the inner cylinder is doubled to 4 mm, how will the capacitance change (see page 1 for choices) ?
c (increase by factor other than 2 or 4).
5) A material (rubber) of dielectric constant 2.3 is inserted between the inner wire and the outer cylinder of the capacitor in problem #4, part a.
a) What will the capacitance be now?
b) How much energy will be stored in this capacitor (with the dielectric) with the 35 volts applied to it?
1.38 x 10-7 J = 138 n Joules.
c) If you double the voltage on this capacitor (from 35 volts to 70 volts), how will the energy stored change (see page 1 for choices) ?
a (increase by factor of 4).
6) You are given three capacitors: C1 = 10 nF; C2 = 5 nF; C3 = 2 nF. They are connected to a 50 volt power supply (VPS) as shown in the diagram.
a) What is the effective capacitance of the three capacitors?
b) What is the effective charge stored on this set of capacitors?
c) If the negative terminal of the battery is grounded (set at 0 volts) so that the positive terminal of the battery is at 50 volts, what is the voltage at the point marked with an x on the diagram?
7) You are given three resistors: 2 W, 5 W, and
a) Draw a diagram showing how to connect the resistors so that you get the smallest effective resistance:
b) Is your connection above purely parallel, purely series, or a combination?
c) Draw a second diagram below showing how to connect the resistors so that you get the largest effective resistance:
d) Draw a third diagram below showing how to connect the resistors so that you get some value between 5 W and 20 W for the effective resistance, and then specify what value you will get:
8) A 4.7 mF capacitor is charged with a power supply of 50 volts. a) What is the maximum charge that this capacitor will store given this voltage (assume a long charging time)?
2.35 x 10-4 Cou. = 235 m Coul.
b) The power supply is then disconnected, and when a switch is thrown the capacitor discharges through a 250 W resistor. How long a time will it take to lose half of the charge that it had stored?
8.14 x 10-4 sec = 0.814 msec.
c) How long a time will it take the capacitor to lose 95% of the initial charge on the capacitor (that is, have only 5% left)?