Question

A series *RLC* circuit has inductance *L* = 12 mH,
capacitance *C* = 1.6 *?*F, and resistance *R*
= 1.5 *?* and begins to oscillate at time *t* =
0.

a) At what time *t*
will the amplitude of the charge oscillations in the circuit be 50%
of its initial value? (Note that we do not know that initial
value.)

b) How many oscillations are completed within this time?

Answer #1

In an L-R-C series circuit, the resistance is 600 ?,
the inductance is 440 mH and the capacitance is 4.00 ?F. At
resonance, the rms current through the circuit is 0.120 A.
(A) Find the resonance frequency f0 of the circuit. [4]
(B) Find the rms voltage of the source. [4] (C) Find the rms
voltage across the capacitor at resonance. [6] (D) Find the rms
voltage across the inductor at resonance.

Consider a simple series RLC circuit with the following values
for the resistance, inductance, and capacitance: R = 110 Ω
(ohms), L = 1 H (henries), and C = 0.001 F
(farads). Furthermore, a battery provides an external voltage,
e(t), into the circuit equal to 7 However, this
external voltage e(t) is not always flowing into
the circuit. Initially, the switch for the circuit is open and
there is no charge or current flowing through the circuit. At time
t...

[Series circuit analogue: RLC circuit with nonzero resistance R
and nonzero voltage E(t) as forcing function is analogous to a
forced damped spring/mass system.] Consider the RLC circuit with
inductance L = 8 henrys, resistance R = 16 ohms, capacitance C =
0.025 farads, and voltage E(t) = 17 cos 2t volts.
(a) Find the current in the circuit for t > 0, given that at
time t = 0 the capacitor is uncharged and there is no current
flowing....

A series RLC circuit has a capacitor with a capacitance of 32.0
?F , an inductor with an inductance of 0.400 H and a resistor with
a resistance of 137 ?. The circuit has a rms current of 5.40 A when
the frequency is 55.0 Hz. What is ?rms, the phase angle
and the average power loss?
The ?rms:
The Phase Angle:
The Average Power Loss:

In an LRC series circuit, the inductance is 244 mH, the
resistance is 29 Ω, and the capacitance is 354 μF. If the
AC voltage applied across the circuit is given by
V(t) = (12 V)sin(11πt)
calculate the voltage across each element at a time of
t = 0.04 s.
VR
=
V
VC
=
V
VL
=
V

A series RLC circuit (L = 24 mH, C = 40 μF,
and R = unknown) has an AC generator with frequency
f = 310 Hz and amplitude Emax = 120 V.
The peak instantaneous current in the circuit is
Imax = 1.4 A.
What is φ = the phase angle between the driving EMF and
the current in the circuit? Define φ to be positive if the
voltage leads the current and φ to be negative if the
current...

Consider an RLC circuit with resistance 21Ω, inductance 0.1H,
capacitance 2500μF, and an impressed voltage, provided by an
alternating current generator, with V=75V, 120Hz.
At t=0 V=0V, Q=4C, I=1A.
a. Complete the ODE below in terms of the charge in the circuit
Q(t): Q’’ + Q’ + Q
L = 0.1 henrys
R = 21 ohms
C = 0.0025 farads
Substitute values in equation: , V = 75V
V
Q” + 210Q’ + 4000Q = 750V
b. Solve the ODE and...

A series RLC circuit has a capacitor with a capacitance of 48.0
uF (microfarads) , an inductor with an inductance of 1.10 H and a
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current of 5.90 A when the frequency is 60.0 Hz. What is
?rms, the phase angle, and the average power loss?

An LC circuit has an
inductance of 20.0 mH and a capacitance of 5.00 mF. At time
t = 0 the charge on the capacitor is 3.0 mC and the
current is 7.0 mA. To what voltage must the capacitor have been
charged before it was attached to the inductor in the LC
circuit?
A) 4.1
V
B) 12
V
C) 9.0
V
D) 1.4
V
E) 0.75 V

This question has 3 parts. A single loop RLC Circuit has
resistance 5.12 Ω, a capacitance 19.3µF, and inductance 998 mH. The
power supply has a peak value of 31.3 V. (a) At what angular
frequency (in rad/s) will the current have it’s maximum value?
(c) At what angular frequency (in rad/s) will the current
amplitude have one-half of this maximum value?

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