In the simple AC circuit shown in Figure , $R=70.0 \Omega$ and $\Delta v=\Delta V_{\max } \sin \omega t$. (a) If $\Delta v_R=0.250 \Delta V_{\max }$ for the first time at $t=0.0100 \mathrm{~s}$, what is the angular frequency of the source? (b) What is the next value of $t$ for which $\Delta v_R=0.250 \Delta V_{\max } ?$

(a) What is the resistance of a lightbulb that uses an average power of 75.0 W when connected to a 60.0-Hz power source having a maximum voltage of 170 V? (b) What is the resistance of a 100-W lightbulb?

An audio amplifier, represented by the AC source and resistor in the figure, delivers to the speaker alternating voltage at audio frequencies. If the source voltage has an amplitude of $15.0 \mathrm{~V}, R=8.20 \Omega$, and the speaker is equivalent to a resistance of $10.4 \Omega$, what is the timeaveraged power transferred to it?

Airports at high elevations have longer runways for takeoffs and landings than do airports at sea level. One reason is that aircraft engines develop less power in the thin air well above sea level. What is another reason?

The toroid as we disscussed earlier consists of $N$ turns and has a rectangular cross section. Its inner and outer radii are $a$ and $b$, respectively. Find the inductance of the toroid.

The switch as we discussed earlier is open for $t<0$ and is then thrown closed at time $t=0$. Find
(a) the current in the inductor

At $t=0$, the open switch as we discussed earlier is thrown closed. We wish to find a symbolic expression for the current in the inductor for time $t>0$. Let this current be called $i$ and choose it to be downward in the inductor in . Identify $i_1$ as the current to the right through $R_1$ and $i_2$ as the current downward through $R_2$.
(a) Use Kirchhoff's junction rule to find a relation among the three currents.

An inductor having inductance L and a capacitor having capacitance C are connected in series. The current in the circuit increases linearly in time as described by i = Kt, where K is a constant. The capacitor is initially uncharged. Determine (a) the voltage across the inductor as a function of time, (b) the voltage across the capacitor as a function of time, and (c) the time when the energy stored in the capacitor first exceeds that in the inductor.

A solenoid of $N_1$ turns has length $l_1$ and radius $R_1$, and a second smaller solenoid of $N_2$ turns has length $l_2$ and radius $R_2$. The smaller solenoid is placed completely inside the larger solenoid so that their long axes coincide. What is the mutual inductance of the two solenoids?

On a printed circuit board, a relatively long straight conductor and a conducting rectangular loop lie in the same plane, as shown in Figure . Taking $h=0.400 \mathrm{~mm}$, $w=1.30 \mathrm{~mm}$, and $L=2.70 \mathrm{~mm}$, find their mutual inductance.

Consider the circuit in Figure P32.17, taking $\mathcal{E}=6.00 \mathrm{~V}$, $L=8.00 \mathrm{mH}$, and $R=4.00 \Omega$. What is the inductive time constant of the circuit?

Consider the circuit shown in the figure. Assuming the inductor in this circuit has the value $L=9.5\ \mathrm{mH}$, how much energy is stored in the inductor after the switch has been closed for a long time?

A self-induced emf in a solenoid of inductance L changes in time as $\boldsymbol{\varepsilon}=\boldsymbol{\varepsilon}_{0} e^{-k t}$. Assuming the charge is finite, find the total charge that passes a point in the wire of the solenoid.

A technician wraps wire around a tube of length 36 cm having a diameter of 8.0 cm. When the windings are evenly spread over the full length of the tube, the result is a solenoid containing 580 turns of wire. Find the self-inductance of this solenoid.