Compute the quality factor for the circuits described in Problems Which circuit has the sharper resonance?

An RLC circuit is used in a radio to tune into an FM station broadcasting at f = 99.7 MHz. The resistance in the circuit is $R=12.0\ \Omega,$ and the inductance is $L= 1.40\ \mu \mathrm{H}.$ What capacitance should be used?

In the clearest terms you can, explain the statement, "The voltage across an inductor leads the current by $90^{\circ} . "$

A radar transmitter contains an LC circuit oscillating at $1.00 \times 10^{10}\ \mathrm{Hz}.$ (a) For a one-turn loop having an inductance of 400 pH to resonate at this frequency, what capacitance is required in series with the loop? (b) The capacitor has square, parallel plates separated by 1.00 mm of air. What should the edge length of the plates be? (c) What is the common reactance of the loop and capacitor at resonance?

A diode is a device that allows current to be carried in only one direction (the direction indicated by the arrowhead in its circuit symbol). Find in terms of $\Delta V$ and $R$ the average power delivered to the diode circuit of the figure.

The tuning circuit of an AM radio contains an $L C$ combination. The inductance is $0.200 \mathrm{mH}$, and the capacitor is variable, so that the circuit can resonate at any frequency between $550 \mathrm{kHz}$ and $1650 \mathrm{kHz}$. Find the range of values required for $C$.

A series circuit consists of an $\mathrm{AC}$ generator with an runs voltage of $120 \mathrm{~V}$ at a frequency of $60.0 \mathrm{~Hz}$ and a magnetic buzzer with a resistance of $100 \Omega$ and an inductance of $100 \mathrm{mH}$.
(a) Find the circuit's power factor.
(b) Suppose a higher power factor is desired. Can a power factor of $1.00$ be achieved by changing the inductance or any other circuit parameters?
(c) Show that a power factor of $1.00$ can be attained by inserting a capacitor into the original circuit, and finding the value of its capacitance.

Energy is to be transmitted at the rate of $20.0 \mathrm{~kW}$ with only $1.00 \%$ loss over a distance of $18.0 \mathrm{~km}$ at potential difference $\Delta V$.
(a) What is the diameter required for each of the two copper wires in the transmission line? Assume the current density is uniform in the conductors.
(b) State how the diameter depends on $\Delta V$.
(c) Evaluate the diameter for $\Delta V=1500 \mathrm{~V}$.
(d) If you choose to make the diameter $3.00 \mathrm{~mm}$, what potential difference is required?

Suppose you manage a factory that uses many electric motors. The motors create a large inductive load to the electric power line as well as a resistive load. The electric company builds an extra-heavy distribution line to supply you with two components of current: one that is $90^{\circ}$ out of phase with the voltage and another that is in phase with the voltage. The electric company charges you an extra fee for “reactive volt-amps” in addition to the amount you pay for the energy you use. You can avoid the extra fee by installing a capacitor between the power line and your factory. The following problem models this solution. In an RL circuit, a 120-V (rms), 60.0-Hz source is in series with a 25.0-mH inductor and a $20.0-\Omega$ resistor. What are (a) the rms current and (b) the power factor? (c) What capacitor must be added in series to make the power factor equal to 1? (d) To what value can the supply voltage be reduced if the power supplied is to be the same as before the capacitor was installed?

Suppose power $\mathscr{P}$ is to be transmitted over a distance $d$ at a voltage $\Delta V$ with only $1.00 \%$ loss. Copper wire of what diameter should be used for each of the two conductors of the transmission line? Assume the current density in the conductors is uniform.

A sinusoidally varying potential difference has amplitude $170 \mathrm{~V}$. (i) What is its minimum instantaneous value?

$$\begin{array}{lllll}\text { (a) } 240 \mathrm{~V} & \text { (b) } 170 \mathrm{~V} & \text { (c) } 120 \mathrm{~V} & \text { (d) } 0 & \text { (e) }-120 \mathrm{~V}\end{array}$$

(f) $-170 \mathrm{~V}$ (g) $-240 \mathrm{~V}$ (ii) What is its average value? (iii) What is its run value? Choose from the same possibilities in each case.

An AC power supply produces a maximum voltage $\Delta V_{\max }=100 \mathrm{~V}$. This power supply is connected to a $24.0-\Omega$ resistor, and the current and resistor voltage are measured with an ideal $\mathrm{AC}$ ammeter and voltmeter, as shown in the figure. What does each meter read? Note that an ideal ammeter has zero resistance and that an ideal voltmeter has infinite resistance.

In a certain series RLC circuit, $I_{\mathrm{rms}}=9.00\ \mathrm{A}, \Delta V_{\mathrm{rms}}= 180\ \mathrm{V},$ and the current leads the voltage by $37.0^{\circ} .$ (a) What is the total resistance of the circuit? (b) Calculate the reactance of the circuit $\left(X_{L}-X_{C}\right).$

A series RLC circuit has a resistance of $45.0 \Omega$ and an impedance of $75.0 \Omega .$ What average power is delivered to this circuit when $\Delta V_{\mathrm{rms}}=210 \mathrm{V}$?