Building an RLC CIRCUIT Building an RLC circuit First, take a 21.0 mu F capacito
ID: 1334836 • Letter: B
Question
Building an RLC CIRCUIT
Building an RLC circuit First, take a 21.0 mu F capacitor and charge it by directly connecting a 6.00 V lantern battery across its two leads (i.e., the wires connected to the two sides of the capacitor). If there were really no resistance in the circuit, the capacitor would become fully charged instantaneously. But a real battery has an "internal resistance" which acts like an actual resistor added to the circuit. A quick web search tells me that a typical lantern battery at room temperature has an internal resistance of about 0.8 Ohm. (The capacitor leads have some resistance too, but much smaller.) So, what is the effective time constant for charging the capacitor in this way? If you leave the battery connected for, say, one second, is that enough time to fully charge the capacitor? (Let's define "fully charged" as being within, say, 0.1% of the asymptotic maximum charge.) When fully charged, how much charge is stored in the capacitor, and how much energy? After removing the battery, you connect the capacitor to an inductor with an inductance value of 8.5 mH. What is the frequency of the oscillations that occur in this circuit? Express your result both as an angular frequency and as a cycles-per-second frequency, with appropriate units for each. If there were really no resistance, the oscillations would continue indefinitely, but again, there is at least a little resistance in the capacitor leads as well as the inductor (which is basically a coil of wire), and this will cause the amplitude of the oscillating current to decay exponentially. If the total resistance is 0.068 Ohm, what is the time constant for the amplitude decay? Now let's put some deliberate resistance into the circuit and see how that changes the oscillations. Disconnect the capacitor and charge it again with the battery, and this time connect it to the 8.5 mH inductor in series with an 8.1 Ohm resistor. Now what is the time constant for the amplitude decay, and what is the frequency of the oscillations?Explanation / Answer
Time Constant is measured in terms of = R x C
= 0.8 * 21.0*10^-6 s
= 16.8 uS
Vc = V(1 – e-t/RC)
Vc = 6*(1 - e^(-0.1/(16.8*10^-6)))
Vc = 5.99
So Yes, the capacitance will be fully charged.
When Fully charged,
Charge Stored in Capacitor,
Q = c*v
Q = 21 uF * 6
Q = 126 uC
Energy in Capacitor, = 0.5 * C*v^2
E = 0.5*21*10^-6 * 6^2
E = 3.78 * 10^-4 J
L = 8.5 * 10^-3 H
C = 21 *10^-6 F
Angular Frequency, w = 1/sqrt(L*C)
w = 1/sqrt(8.5 * 10^-3 * 21 *10^-6 )
w = 2367 rad/sec
Angular Frequency, w =2367 rad/sec
Frequency, f = w/2*pi
f = 2367/(2*3.14)
f = 377 hz
Frequency, f = 377 hz
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.