Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

Solutions 255

whose edges contain six identical capacitors.
Therefore, we conclude from the symmetry con-
siderations that irrespective of the pair of points
between which the current source is connected,
there always exists an uncharged capacitor in the
circuit (the capacitor in the edge crossed with
the edge containing the source). For example, if
the current source is connected between points A
and B in Fig. 209, the capacitor between points C
and D will be uncharged since the potentials of
points C and D are equal.
3.14. The capacitance of the nonlinear capacitor is
C = sCo = aUC 0 ,

where Co is the capacitance of the capacitor without

a dielectric. The charge on the nonlinear capacitor

is qn = CU = aCo U 2 , while the charge on the

normal capacitor is qo = Co U. It follows from the
charge conservation law

qn qo = Co Uo

that the required voltage is

4aU 0 + 1 — 1

U — (^) 12 V.
2a
3.15. Let us go over to the inertial reference frame
fixed to the moving centre of the thread. Then
the balls have the same velocity u at the initial
instant. The energy stored initially in the system is
q2 2mu2

• W1 4:18 0 .2/ 2 •
  At the moment of the closest approach, the energy
  of the system is
  . =
  W$ a 47tgod •
  Using the energy conservation law, we find that

d—

21q 2

q 2 -1- 87teomv 2 1 •