14.6 RLC Series Circuits

In an RLC circuit, $L = 5.0 \text{mH} , C = 6.0 \mu \text{F} , \text{and} R = 200 \Omega .$ (a) Is the circuit underdamped, critically damped, or overdamped? (b) If the circuit starts oscillating with a charge of $3.0 \times 10^{−3} \text{C}$ on the capacitor, how much energy has been dissipated in the resistor by the time the oscillations cease?

Describe what effect the resistance of the connecting wires has on an oscillating LC circuit.

A radio receiver uses an RLC circuit to pick out particular frequencies to listen to in your house or car without hearing other unwanted frequencies. How would someone design such a circuit?

In an oscillating RLC circuit with $L = 10 \text{mH} , C = 1.5 \mu \text{F} , \text{and} R = 2.0 \Omega ,$ how much time elapses before the amplitude of the oscillations drops to half its initial value?

Show that the self-inductance per unit length of an infinite, straight, thin wire is infinite.

A solenoid with $4 x 10^{7}$ turns/m has an iron core placed in it whose magnetic susceptibility is $4.0 \times 10^{3}$. (a) If a current of 2.0 A flows through the solenoid, what is the magnetic field in the iron core? (b) What is the effective surface current formed by the aligned atomic current loops in the iron core? (c) What is the self-inductance of the filled solenoid?

A 25.0-H inductor has 100 A of current turned off in 1.00 ms. (a) What voltage is induced to oppose this? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

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.

$\frac{d U}{d t} = −2 \beta U ,$ where $\beta = \frac{R}{2 L} .$

(b) Using the definition of the Q-factor as energy divided by the loss over the next cycle, prove that…