Chapter 32: AC Circuits

You have a resistor and a capacitor of unknown values. First, you charge the capacitor and discharge it through the resistor. By monitoring the capacitor voltage on a oscilloscope, you see that the voltage decays to half its initial value in $2.5ms$. You then use the resistor and capacitor to make a low-pass filter. What is the crossover frequency $f_c$?

Figure P$32.47$shows a parallel RC circuit.

a. Use a phasor-diagram analysis to find expressions for the peak currents $I_R$and $I_C$.

b. Complete the phasor analysis by finding an expression for the peak emf current I.

The small transformers that power many consumer products produce a$12.0V_{rms}$, $60Hz$emf. Design a circuit using resistors and capacitors that uses the transformer voltage as an input and produces a $6.0V_{rms}$ output that leads the input voltage by $45°$.

Use a phasor diagram to analyze the RL circuit of FIGURE P$32.49$. In particular,

a. Find expressions for $I,V_{R}and{V}_L$.

b. What is VR in the limits $\omega \to 0$and $\omega \to \infty$?

c. If the output is taken from the resistor, is this a low-pass or a high-pass filter? Explain.

d. Find an expression for the crossover frequency ${\omega }_C$.

An inductor is connected across an oscillating emf. The peak current through the inductor is $2.0$A. What is the peak current if:

a. The inductance $L$is doubled?

b. The peak emf $E_0$is doubled?

c. The frequency $V$is doubled?

Figure shows voltage and current graphs for a resistor.

a. What is the emf frequency $f$?

b. What is the value of the resistance $R$?

c. Draw the resistor’s voltage and current phasors at $t=15ms$

A series $RL$circuit is built with a role="math" localid="1650111235060" $110\Omega$resistor and a $5.0-cm-$ long,$1.0-cm-$diameter solenoid with $800$turns of wire. What is the peak magnetic flux through the solenoid if the circuit is driven by a $12V,5.0kHz$source?

A series$RLC$ circuit consists of a$75\Omega$resistor, a $0.12H$ inductor, and a $30mF$ capacitor. It is attached to a$120V/60Hz$ power line. What are (a) the peak current$I$, (b) the phase angle $\varphi$, and (c) the average power loss?

A series$RLC$circuit consists of a $25\Omega$resistor, a $0.10H$inductor, and a$100mF$capacitor. It draws a$2.5A$$rms$current when attached to a $60Hz$source. What are (a) the $emf$$E_{rms}$, (b) the phase angle$\varphi$and (c) the average power loss?

A series RLC circuit consists of a $550\Omega$resistor, a $2.1mH$ inductor, and a $550nF$ capacitor. It is connected to a $50V$ rms oscillating voltage source with an adjustable frequency. An oscillating magnetic field is observed at a point $2.5mm$ from the center of one of the circuit wires, which is long and straight. What is the maximum magnetic field amplitude that can be generated?