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

Solutions 289

Therefore, the amplitude of the voltage across the
capacitor plates is
W 0 (aL
U 0 —
R •

3.60. During steady-state oscillations, the work

done by the external source of current must be

equal to the amount of.heat liberated in the re-

sistor. For this the amplitudes of the external

voltage and the voltage across the resistor must be

equal: R/ 0 = U 0. Since the current in the circuit

and the charge on the capacitor are connected

through the equation I = dq/dt, the amplitudes

/ 0 and q 0 of current and charge can be obtained

from the formula

/ 0 =---

where the resonance frequency is co 0 = 1/1/ LC.

By hypothesis,

U 0 =-- U —

qi

C '

whence

• 7 /? C 'I" c •

3.61. For 0 < t < x, charge oscillations will

occur in the circuit, and

CU )

q --= (-- (^2) -- cos coot,

1/ 2

w°— _ V 77a-.

At the instant T, the charge on the capacitor at its

breakdown is (CU/2) cos coot, and the energy of

the capacitor is (CU 2 /8) cost coot. After the break-

down, this energy is converted into heat and lost

by the system. The remaining energy is

W

CU (^2) CU 2
cost evr.
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