A motor may be modeled as a series $R L$ circuit. A particular motor operates from an ordinary $60~\mathrm{Hz}$ wall outlet with $\mathcal{E}_{\mathrm{rms}}=115 \mathrm{~V}$. The motor draws a current of $I_{\mathrm{rms}}=2.5 \mathrm{~A}$. If the effective resistance is $R=16 \Omega$, what is the inductive reactance of the circuit? What is the value of the inductance?

A radio receiver contains an $L C$ circuit whose natural frequency of oscillation can be adjusted, or tuned, to match the frequency of incoming radio waves. The adjustment is made by means of a variable capacitor. Suppose that the inductance of the circuit is $15 \mu \mathrm{H}$. Over what range of capacitances must the capacitor be adjustable if the frequencies of oscillation of the circuit are to span the range from $530 \mathrm{kHz}$ to $1600 \mathrm{kHz}$ ?

You want to construct an $L C$ circuit of natural frequency $8.0 \times 10^3 \mathrm{~Hz}$. You have available a capacitor of $0.20 \mu \mathrm{F}$. What inductor do you need?

The GG-$1$ electric locomotive develops $4600 \mathrm{hp}$; it runs on an rms AC voltage of $1100 \mathrm{~V}$. $(a)$ What rms current does this locomotive draw? $(b)$ Why is it advantageous to supply the electric power for locomotives at high voltage (and fairly low current)?

Some electric motors operate only on DC, others only on AC. What is the difference between these motors?

What is the natural frequency for an $L C$ circuit consisting of a $2.2 \times 10^{-6} \mathrm{~F}$ capacitor and an $8.0 \times 10^{-2} \mathrm{H}$ inductor?

An inductor is built in the shape of a solenoid of radius $0.20$ $\mathrm{cm}$, length $4.0 \mathrm{~cm}$, with 1000 turns. This inductor is connected to a generator supplying an rms voltage of $1.2 \times 10^{-4}$ $\mathrm{V} \mathrm{AC}$ at an angular frequency of $9.0 \times 10^3$ radians $/ \mathrm{s}$. $(a)$ What is the inductance? Assume that the solenoid can be treated as very long. $(b)$ What is the rms current flowing through the inductor? $(c)$ What is the rms energy stored in the inductor?

An inductor of $4.5 \times 10^{-2} \mathrm{H}$ and a capacitor of $0.25 \mu \mathrm{F}$ are connected in parallel to a source of alternating emf of frequency $\omega$. For what value of $\omega$ will the rms currents in the inductor and the capacitor be of equal magnitudes?

A $2.0~\mu \mathrm{F}$ capacitor and a $3.0~\mathrm{mH}$ inductor are connected in parallel with an AC power supply. At what frequency will the inductive reactance be $3$ times the capacitive reactance?

An inductor with $L=4.0 \times 10^{-2} \mathrm{H}$ is connected to a source of alternating emf. This source provides an $\operatorname{emf} \mathcal{E}=\mathcal{E}_{\max } \times$ $\cos \omega t$, with $\mathcal{E}_{\max }=0.20 \mathrm{~V}$ and $\omega=6.0 \times 10^3$ radians $/ \mathrm{s}$. $(a)$ What is the reactance of the inductor? $(b)$ What is the maximum current in the circuit? $(c)$ What is the current at time $t=0$ ? At time $t=\pi / 4 \omega$ ?

To prevent radio frequency interference in electronic equipment, inductors are often placed wherever the transmission of only low-frequency signals is desired. If such an rf choke has an inductance of $47 \mu \mathrm{H}$, what reactance does it present to a $60~\mathrm{Hz}$ power supply current? To a $100~\mathrm{MHz}$ radio signal?

An AM radio antenna has the shape of a coil with inductance $0.90 \mathrm{mH}$. A radio wave with frequency $1.2 \mathrm{MHz}$ induces a current of amplitude $5.2 \mathrm{nA}$ in the coil. What is the amplitude of the induced voltage across the coil?

An electric heater operates from $60~\mathrm{Hz}, 115~\mathrm{V} \mathrm{AC}$. When standing near the heater, why do we not feel $120$ heat pulses per second?

A high-voltage power line operates on an rms voltage of 230000 volts $\mathrm{AC}$ and delivers an rms current of $740 \mathrm{~A}$ to a resistive load. $(a)$ What are the maximum instantaneous voltage and current? $(b)$ What are the maximum instantaneous power and the average power delivered?