In a damped oscillating circuit the energy is dissipated In the resistor. The Q-factor Is a measure of the persistence of the oscillator against the dissipative loss. (a) Prove that for a ligt1y danced circuit the energy, U, in the circuit decreases according to the following equation. d u d t = − 2 β u , w h e r e β = R 2 L (b) Using the definition of the Q-factor as energy divided by the loss over the next cycle, prove that Q-factor of a lightly damped oscillator as defined in this problem is Q = U b e g i n △ U o n e c y c l e = 1 R L C c (Hint: For (b), to obtain Q, divide E at the beginning of one cycle by the change E over the next cycle.)
In a damped oscillating circuit the energy is dissipated In the resistor. The Q-factor Is a measure of the persistence of the oscillator against the dissipative loss. (a) Prove that for a ligt1y danced circuit the energy, U, in the circuit decreases according to the following equation. d u d t = − 2 β u , w h e r e β = R 2 L (b) Using the definition of the Q-factor as energy divided by the loss over the next cycle, prove that Q-factor of a lightly damped oscillator as defined in this problem is Q = U b e g i n △ U o n e c y c l e = 1 R L C c (Hint: For (b), to obtain Q, divide E at the beginning of one cycle by the change E over the next cycle.)
In a damped oscillating circuit the energy is dissipated In the resistor. The Q-factor Is a measure of the persistence of the oscillator against the dissipative loss. (a) Prove that for a ligt1y danced circuit the energy, U, in the circuit decreases according to the following equation.
d
u
d
t
=
−
2
β
u
,
w
h
e
r
e
β
=
R
2
L
(b) Using the definition of the Q-factor as energy divided by the loss over the next cycle, prove that Q-factor of a lightly damped oscillator as defined in this problem is
Q
=
U
b
e
g
i
n
△
U
o
n
e
c
y
c
l
e
=
1
R
L
C
c
(Hint: For (b), to obtain Q, divide E at the beginning of one
In a damped oscillating circuit the energy is dissipated in the resistor. The Q-factor is a measure of the persistence of the oscillator against the dissipative loss. (a) Prove that for a lightly damped circuit the energy, U, in the circuit decreases according to the following equation. dU dt = −2βU, where β = R2L . (b) Using the definition of the Q-factor as energy dividedby the loss over the next cycle, prove that Q-factor of a lightly damped oscillator as defined in this problem is Q ≡ Ubegin ΔUone cycle = 1 R L C. (Hint: For (b), to obtain Q, divide E at the beginning of one cycle by the change ΔE over the next cycle.)
A 7.50 nF capacitor is charged to 12.0 V, then disconnectedfrom the power supply and connected in series through a coil. The periodof oscillation of the circuit is then measured to be 8.60 * 10^-5 s.Calculate:the total energy of the circuit
What is the capacitance of an oscillating LC circuit if the maximum charge on the capacitor is 1.60 mC and the total energy is 140 mJ?
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