Exam 19: Dc Circuits

A $3.0 - \Omega$ resistor is connected in parallel with a $6.0 - \Omega$ resistor. This combination is then connected in series with a $4.0 - \Omega$ resistor. The resistors are connected across an ideal 12-volt battery. How much power is dissipated in the $3.0 - \Omega$ resistor?

The figure shows a circuit. The ideal battery has a constant terminal voltage of $\varepsilon = 27 \mathrm {~V}$ , the inductance is $L = 0.40 \mathrm { H }$ , and the resistances are $R _ { 1 } = 12 \Omega$ and $R _ { 2 } = 9.0 \Omega$ . Initially the switch $\mathrm { S }$ is open with no currents flowing. Then the switch is suddenly closed. (a) What is the current in the resistor $R _ { 1 }$ the instant after the switch is closed? (b) After leaving the switch has been closed for a very long time, it is opened again. Just after it is opened, what is the current in $R _ { 1 }$ ?

A multiloop circuit is shown in the figure. Find the emf $\varepsilon _ { 1 }$ if the batteries are ideal. (It is not necessary to solve the entire circuit.)

A 4.0- $\Omega$ resistor is connected to a $12 - \Omega$ resistor and this combination is connected to an ideal dc power supply with voltage $V$ as shown in the figure. If the total current in this circuit is $I = 2.0 \mathrm {~A}$ , what is the value of voltage $V$ ?

A charged capacitor is connected in series with a resistor and an open switch. At time t = 0 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?

A network of capacitors is connected across a potential difference $V _ { 0 }$ as shown in the figure. (a) What should $V _ { 0 }$ be so that the $60.0 - \mu \mathrm { F }$ capacitor will have $18.0 \mu \mathrm { C }$ of charge on each of its plates? (b) Under the conditions of part (a), how much total energy is stored in this network of capacitors?

A 5.0- $\mu \mathrm { F }$ and a 12.0- $\mu \mathrm { F }$ capacitor are connected in series, and the series arrangement is connected in parallel to a 29.0- $\mathrm { F }$ capacitor. How much capacitance would a single capacitor need to replace this combination of three capacitors?

What is the power output in an ac series circuit with $12.0 \Omega$ of resistance, $15.0 \Omega$ of inductive reactance, and $10.0 \Omega$ of capacitive reactance, when the circuit is connected to a $120 - \mathrm { V }$ rms power supply?

A $120 - \mathrm { V }$ rms voltage is applied across a $6.00 - \mu \mathrm { F }$ capacitor and a $100 - \Omega$ resistor. If the frequency of the generator is $60.0 \mathrm {~Hz}$ , what is the impedance of this circuit?

An electromagnetic flowmeter is useful when it is desirable not to interrupt the system in which the fluid is flowing (such as the blood in an artery during heart surgery). Such a device is illustrated in the figure. The conducting fluid moves with speed $v$ in a tube of diameter $d$ . Perpendicular to this tube is a magnetic field B. A voltage $V$ is induced between opposite sides of the tube due to the motion of the conducting fluid in the magnetic field. For a certain case, $B =$ $0.120 \mathrm {~T} , d = 1.2 \mathrm {~cm}$ , and the measured voltage is $V = 2.88 \mathrm { mV }$ . Determine the speed of the fluid.

The phase angle of a series $R L$ ac circuit with a $100 - \Omega$ resistor and a $20.0 - \mathrm { mH }$ inductor is $70.0 ^ { \circ }$ . What is the inductive reactance of this circuit?

Four resistors having resistances of $20 \Omega , 40 \Omega , 60 \Omega$ , and $80 \Omega$ are connected in series across an ideal $50 - \mathrm { V }$ dc source. What is the current through each resistor?

The inductor in a radio receiver carries a current of amplitude $0.200 \mathrm {~A}$ when an ac voltage of amplitude $2.40 \mathrm {~V}$ is across it at a frequency of $1400 \mathrm {~Hz}$ . What is the value of the inductance?

Coil $\mathrm { A }$ is close to, but not touching, coil B. If a steady counterclockwise $100 - \mathrm { A }$ current flows in coil A, what can you say about the induced current in coil B?

A flux of $4.0 \times 10 ^ { - 5 } \mathrm {~T} \cdot \mathrm { m } ^ { 2 }$ is maintained through a coil of area $7.5 \mathrm {~cm} ^ { 2 }$ for $0.50 \mathrm {~s}$ . What emf is induced in this coil during this time by this flux?

A bar magnet is oriented above a copper ring, as shown in the figure. If the magnet is pulled upward, what is the direction of the current induced in the ring, as viewed from above?

In the circuit shown in the figure, the $60 - \mathrm { Hz }$ ac source has a voltage amplitude of $120 \mathrm {~V}$ , the capacitive reactance is $920 \Omega$ , the inductive reactance is $290 \Omega$ , and the resistance is $420 \Omega$ . What is the rms current in the circuit?

A flat square coil of wire with 15 turns and an area of $0.40 \mathrm {~m} ^ { 2 }$ is placed with the plane of its area parallel to a magnetic field of $0.75 \mathrm {~T}$ . The coil is flipped so its plane is perpendicular to the magnetic field in a time of $0.050 \mathrm {~s}$ . What is the magnitude of the average induced emf in the coil?

What is the resonance frequency of a series ac circuit consisting of a $40.0 \mu \mathrm { F }$ capacitor, a $55 - \Omega$ resistor, and a $0.030 \mathrm { H }$ inductor?

A flat circular loop of radius 0.10 m is rotating in a uniform magnetic field of 0.20 T. Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are Perpendicular.