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Physics 2220
Second Exam
Summer 2014
(Chs 27-30)
Wednesday 2 July
Name:
Adam Payne (JFB 102)
Circle your Discussion TA:
Mei Hui Teh (LCB 2 1 5)
Chris Winterowd (LCB 225)
You may use your one sheet of notes and formulas, but you must not collaborate with any
other person. Do all three problems, showing your method and working clearly (a correct answer
alone is not necessarily sufficient). Be sure to include correct SI units in your answers where
appropriate. The number of marks for each part is given in square brackets, [ ], to its right,
1. (a) A cylindrical wire of cross-sectional area A, length £ , resistivity p, and resistance R is
made of material that is ductile (i.e., pliable, not brittle). If this wire is drawn out into a new
cylindrical wire having one-third the radius of the original wire, find its new resistance, R',
giving the answer as a multiple of R. (Assume that both the resistivity and the volume of the
wire are left unchanged by the drawing process.)
[8]
(b) Suppose that the resistivity of copper is 1.7 x 10~ 8 Q-m at room temperature (20 °C),
and that its temperature coefficient of resistivity is a = 3.9 x 10~3 (°C)~1. When a coil of copper
wire at temperature T is connected to a 12-V battery of negligible internal resistance, the current
in the coil is found to be one-third less than it was when the same coil at room temperature was
connected to the same battery. Calculate the value of T correct to the nearest degree.
[8]
(c) A certain battery is found to have a terminal potential difference of 1 7 V when it supplies
a current of 2.0 A, but when the same battery supplies a current of 8.0 A its terminal potential
difference is only 14 V. Calculate the emf, S, and the internal resistance, r, of this battery.
[8]
(d) When two resistors are connected in series their equivalent resistance is 50 Q, and when
they are connected in parallel their equivalent resistance is 8.0 Q. What are their resistances? [8]
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Physics 2220, Summer 2014
Name:
Second Exam
Circle TA:
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The sketch at the right shows a circuit containing a
battery of emf S and negligible internal resistance, a switch
S that is initially open, a capacitor of capacitance C that is
initially uncharged, and resistors RI, R2,
(a) The switch S is now closed at time t = 0. In terms
of the charge Q on the capacitor, the quantities defined
above, and the currents I], 12, and Is shown in the sketch,
use Kirchhoff's rules to write down (but do not solve) a
system of three simultaneous equations that would allow us
to find the three unknown currents.
[8]
(b) Now, assuming that S = 72.0 V, C = 8.00 jiF, RI = 2.00 Q, R2 = 12.0 Q, and R3 = 6.00 Q,
find the value of the current Is through the 6.00 Q, resistor at each of the following times:
(i) t = 0 (just after the switch is closed); [9]
(ii) t = °o (after a very long time).
(You still do not need to solve the equations in part a.)
[3]
(c) After the switch has been closed for a long time, it is reopened at a time we again call t = 0.
(i) How long will it take for the charge on the capacitor to be reduced to one-fifth of its
initial value?
[4]
(ii) What will be the maximum current through the resistor R2, and which direction will
it flow ('up' or 'down' in the sketch)?
[6]
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Second Exam
Circle TA:
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3. (a) Suppose that particle B has twice the charge and twice the mass of particle A. (For
example, A might be a deuteron and B an alpha particle - that is, a helium nucleus.) Each of
these particles is to be accelerated in the same cyclotron, using the same magnetic field.
(i) How would the values of the cyclotron frequency, co, compare for the two different
particles?
[4]
(ii) How would their kinetic energies compare when they left the cyclotron? Be as specific as
possible.
[6]
(b) A long, solid, cylindrical conductor of radius R carries electric current along its length. The
current density magnitude, J, however, is not uniform over the cross-section of the conductor but
is a function of the radius according to J = kr3 (for 0 < r < R), where k is a positive constant
(not the Coulomb constant), and r is the radial distance from the axis of the cylinder.
(i) What are the SI units of k?
[2]
(ii) In terms of k, r, R, and u.0, use Ampere's law to calculate the magnitude of:
• the magnetic field for r < R (inside the cylinder);
• the magnetic'field for r > R (outside the cylinder).
[12]
[6]
(iii) If an electron outside the cylinder moves parallel to the axis of the cylinder in the same
direction as the current, and a proton outside the cylinder moves perpendicular to the surface of
the cylinder in a direction radially outwards, specify clearly the directions of the magnetic forces
(if any) that will act on each of those particles.
[8]
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