Exam 19: Dc Circuits

Five $2.0 - \Omega$ resistors are connected as shown in the figure. What is the equivalent resistance of this combination between points $a$ and $b$ ?

The figure shows a solenoid having no appreciable resistance. When the current in this solenoid is decreasing at a rate of $5.5 \mathrm {~A} / \mathrm { s }$ , the self-induced emf in the solenoid is measured to be $9.5 \mathrm {~V}$ . ((a) What is the self-inductance of this solenoid? (b) If the current is in the direction from $b$ to $a$ in the figure, which point, $a$ or $b$ , is at higher potential?

A $50 - \Omega$ resistor is placed in series with a $40 - \mathrm { mH }$ inductor. At what frequency will the current in this circuit lag the applied voltage by exactly $45 ^ { \circ }$ ?

A long vertical wire carries a steady $70 \mathrm {~A}$ current. As shown in the figure, a pair of horizontal rails are $0.20 \mathrm {~m}$ apart. $\mathbf { A } 20 - \Omega$ resistor connects points $a$ and $b$ , at the end of the rails. $\mathbf { A }$ bar is in contact with the rails, and is moved by an external force with a constant horizontal velocity of $0.90 \mathrm {~m} / \mathrm { s }$ to the right, as shown. The bar and the rails have negligible resistance. At the instant that the bar is $0.20 \mathrm {~m}$ from the wire, what are the induced current in the resistor and its direction through the resistor? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

What rms current flows in a $60 - \mathrm { mH }$ inductor when $120 - \mathrm { V }$ rms ac at a frequency of $20 \mathrm { kHz }$ is applied to it?

An alternating current is supplied to an electronic component with a rating that the voltage across it can never, even for an instant, exceed $16 \mathrm {~V}$ . What is the highest rms voltage that can be supplied to this component while staying below the voltage limit?

A $120 - \mathrm { V }$ rms voltage at $60.0 \mathrm {~Hz}$ is applied across a capacitor and a $100 - \Omega$ resistor. If the impedance of this circuit is $200 \Omega$ , what is the average power of this circuit?

The current flowing through a circuit is changing at a rate of $6.0 \mathrm {~A} / \mathrm { s }$ . If the circuit contains a $190 - \mathrm { H }$ inductor, what is the emf across the inductor?

A capacitor with a capacitive reactance of $40.0 \Omega$ is connected in series with a $100 - \Omega$ resistor across an ac source of frequency $60.0 \mathrm {~Hz}$ . What is the phase angle?

A simple ac circuit is composed of a capacitor connected across the terminals of an ac power source. If the frequency of the source is doubled, what happens to the reactance of the capacitor?

An uncharged capacitor is connected in series with a resistor, a dc battery, and an open switch. At time $t = 0 \mathrm {~s}$ , the switch is closed. Which of the graphs below best describes the potential difference $V$ across the resistor as a function of time $t$ ?

An ac generator consisting of a coil with $N$ turns rotating at angular speed $\omega$ in an external magnetic field $B$ produces a maximum emf $\varepsilon _ { 0 }$ . If you now decrease the number of turns in the coil to $N / 2$ and at the same time cause it to rotate twice as fast, what will be the new maximum emf if you do not change any of the other quantities?

An ac generator contains 80 flat rectangular loops of wire, each of which is $12 \mathrm {~cm}$ long and $8 \mathrm {~cm}$ wide. The loops rotate at $1200 \mathrm { rpm }$ about an axis through the center and parallel to the long side. If the magnetic field in which the loop rotates is uniform, has magnitude $0.30 \mathrm {~T}$ , and is perpendicular to the axis of rotation, what will be the maximum output voltage of this generator?

As shown in the figure, a region of space contains a uniform magnetic field. The magnitude of this field is $2.8 \mathrm {~T}$ , and it is directed straight into the plane of the page in the region shown. Outside this region the magnetic field is zero. A rectangular loop measuring $0.20 \mathrm {~m}$ by $0.60 \mathrm {~m}$ and having a resistance of $2 \Omega$ is being pulled into the magnetic field by an external force, as shown. (a) What is the direction (clockwise or counterclockwise) of the current induced in the loop? (b) Calculate the magnitude of the external force $F _ { \text {ext } }$ that is required to move the loop at a constant speed of $3.9 \mathrm {~m} / \mathrm { s }$ .

A 120-V rms signal at $60 \mathrm {~Hz}$ is applied across a series combination of a $30 - \mathrm { mH }$ inductor and a $100 - \Omega$ resistor. What is the rms value of the current in this circuit?

The wire in the figure carries a steady current $I$ . What is true about the currents induced in each of the three loops shown? The wire and the three loops are all in the same plane.

A series circuit has a sinusoidal voltage supplied to it at $632 \mathrm { kHz }$ with a peak voltage of $748 \mathrm {~V}$ . It also contains a 25-k $\Omega$ resistance, a $16 - \mu \mathrm { F }$ capacitance, and a $30 - \mathrm { H }$ inductance. What is the peak current for this circuit?

For the circuit shown in the figure, write the Kirchhoff current equation for the node labeled A. Notice the directions of the currents!

The circuit power factor of an $R C$ circuit is $0.620$ . The rms value of the ac voltage applied to this signal is $120 \mathrm {~V}$ and the impedance is $200 \Omega$ . What is the average power of this circuit?

As shown in the figure, a straight wire carries a steady current $I$ . A metal bar is in contact with a pair of rails and is in upward motion with velocity of magnitude $v$ . The polarity of the induced emf in terminals $X$ and $Y$ is