A resistor R, inductor L, and capacitor C are connected in series to an AC source of rms voltage $\Delta V$ and variable frequency. If the operating frequency is twice the resonance frequency, find the energy delivered to the circuit during one period.

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?

The LC circuit of a radar transmitter oscillates at 9.00 GHz (a) What inductance is required for the circuit to resonate at this frequency if its capacitance is 2.00 pF? (b) What is the inductive reactance of the circuit at this frequency?

Write the expression in the form $x^n$. $\sqrt[3]{x}$

You are working in a factory and have been tasked with determining the electrical needs for a new motor that will be installed on an assembly line. The motor has been tested under load conditions and found to have a resistance of $35.0 \Omega$ and an inductive reactance of $50.0 \Omega$. We can model the motor as a series RL circuit. The motor will have its own dedicated circuit with an rms voltage of 480 V. You need to determine the peak current drawn by the motor to determine the size of the circuit breaker needed to protect the circuit.

The circuit shown in Figure has a current source as shown in Figure Determine the current $i(t)$ in the inductor.

Determine the inductor current, $i(t)$, in the circuit shown in Figure

Find the length of the following polar curves. The spiral $r=2 e^{2 \theta}$, for $0 \leq \theta \leq \ln 8$.

A lightbulb marked "75 W [at] 120 V" is screwed into a socket at one end of a long extension cord, in which each of the two conductors has resistance $0.800 ~ \Omega$. The other end of the extension cord is plugged into a $120$-V outlet.

(a) Explain why the actual power delivered to the lightbulb cannot be 75 W in this situation.

(b) Draw a circuit diagram.

(c) Find the actual power delivered to the lightbulb in this circuit.

A source delivers an AC voltage of the form $\Delta v= 98.0 \sin 80 \pi t,$ where $\Delta v$ is in volts and t is in seconds, to a capacitor. The maximum current in the circuit is 0.500 A. Find (a) the rms voltage of the source, (b) the frequency of the source, and (c) the value of the capacitance.

Suppose a series $L R C$ circuit has two resistors, $R_1$ and $R_2$, two capacitors, $C_1$ and $C_2$, and two inductors, $L_1$ and $L_2$, all in series. Calculate the total impedance of the circuit.

In an RLC series circuit that includes a source of alternating current operating at fixed frequency and voltage, the resistance R is equal to the inductive reactance. If the plate separation of the parallel-plate capacitor is reduced to one-half its original value, the current in the circuit doubles. Find the initial capacitive reactance in terms of R.

The voltage V, in volts, produced by an ac generator at time t, in seconds, is $V(t)=220 \sin (120 \pi t).$ What is the amplitude and period of the current I?

An AC source with $\Delta V_{\max }=150 \mathrm{~V}$ and $f=50.0 \mathrm{~Hz}$ is connected between points $a$ and $d$ in Figure P33.26. Calculate the maximum voltages between points (a) $a$ and $b$, (b) $b$ and $c$, (c) $c$ and $d$, and (d) $b$ and $d$.