Exam 19: Dc Circuits

A $2.0 - \mu \mathrm { F }$ capacitor that is initially uncharged is charged through a $50 - \mathrm { k } \Omega$ resistor. How long does it take for the capacitor to reach $90 \%$ of its full charge?

A series circuit consists of an ac voltage source of frequency $60 \mathrm {~Hz}$ and source voltage amplitude $345 \mathrm {~V}$ , a resistor of resistance $393 \Omega$ , a capacitor of capacitance $2.7 \times 10 ^ { - 6 } \mathrm {~F}$ , and an inductor of inductance $L$ . (a) What must be the value of $L$ for the phase angle of the circuit to be zero? (b) When $L$ has the value calculated in part (a), what is the current amplitude in the circuit?

Three light bulbs, A, B, and C, have electrical ratings as follows: Bulb A: $96.0 \mathrm {~W} , 1.70 \mathrm {~A}$ Bulb B: $80.0 \mathrm {~V} , 205 \mathrm {~W}$ Bulb C: $120 \mathrm {~V} , 0.400 \mathrm {~A}$ These three bulbs are connected in a circuit across a $150 - \mathrm { V }$ voltage power source, as shown in the figure. Assume that the filament resistances of the light bulbs are constant and independent of operating conditions. What is the equivalent resistance of this combination of bulbs between the terminals of the power source?

A series circuit has a $50 - \mathrm { Hz }$ ac source, a $40 - \Omega$ resistor, a $0.70 - \mathrm { H }$ inductor, and a $60 - \mu \mathrm { F }$ capacitor, as shown in the figure. The rms current in the circuit is $1.6 \mathrm {~A}$ . What is the voltage amplitude of the source?

A $0.150 - \mathrm { kW }$ lamp is plugged into a $120 - \mathrm { V }$ ac wall outlet. What are (a) the peak current through the lamp, (b) the rms current through the lamp, and (c) the resistance of the lamp?

A multiloop circuit is shown in the figure, but some quantities are not labeled. Find the current $I _ { 1 }$ if the batteries are ideal. (It is not necessary to solve the entire circuit.)

Each of the resistors shown in the figure has a resistance of $180.0 \Omega$ . What is the equivalent resistance between points $a$ and $b$ of this combination?

What is the equivalent resistance of the circuit shown in the figure? The battery is ideal and all resistances are accurate to 3 significant figures.

An ideal transformer with 120 turns in its secondary supplies 12 V at 220 mA to a toy train. The primary is connected across a 120-V wall outlet. (a) How many turns are in the primary? (b) What is the primary current? (c) What power is delivered by the wall outlet?

For the circuit shown in the figure, the ideal battery has an emf $\varepsilon = 80 \mathrm {~V}$ . The four resistors have resistances of $R _ { 1 } = 14 \Omega , R _ { 2 } = 21 \Omega , R _ { 3 } = 21 \Omega$ , and $R _ { 4 } = 14 \Omega$ . Calculate the rate at which heat is being generated in the resistor $R _ { 4 }$ .

A battery has an emf $\varepsilon = 78.0 \mathrm {~V}$ and an internal resistance $r = 4.0 \Omega$ , as shown in the figure. A current of $4.7 \mathrm {~A}$ is drawn from the battery when a resistor $R$ is connected across the terminals a and $b$ . The power dissipated by the resistor $R$ is closest to

A conducting rod whose length is $\ell = 1.60 \mathrm {~m}$ is placed on frictionless $U$ -shaped metal rails that is connected to a lightbulb having a resistance of $4.00 \Omega$ as shown in the figure. The rails and the rod are in the plane of the page. A constant uniform magnetic field of strength $2.20 \mathrm {~T}$ is applied perpendicular to and out of the paper. What is the magnitude of the external applied force needed to move the rod to the right with a constant speed of $6.00 \mathrm {~m} / \mathrm { s }$ ?

A $120 - V$ rms voltage is applied across a $6.0 - \mu \mathrm { F }$ capacitor and a series combination of a $100 - \Omega$ resistor. If the frequency of the power source is $60 \mathrm {~Hz}$ , what is the rms value of the current in the circuit?

A 4.0- $\Omega$ resistor is connected with a 12- $\Omega$ resistor and both of these are connected across 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 current through the $4.0 - \Omega$ resistor?

Four resistors are connected across an ideal dc battery with voltage $V$ as shown in the figure. Assume that all quantities shown are accurate to two significant figures. If the total current through this circuit is $I = 2.0 \mathrm {~A}$ , what is the current through the $4.0 - \Omega$ resistor?

A rectangular loop of wire that can rotate about an axis through its center is placed between the poles of a magnet in a magnetic field with a strength of $0.40 \mathrm {~T}$ , as shown in the figure. The length of the loop $L$ is $0.16 \mathrm {~m}$ and its width $w$ is $0.040 \mathrm {~m}$ . What is the magnetic flux through the loop when the plane of the loop makes an angle of $60 ^ { \circ }$ with the magnetic field?

A bar magnet is oriented above a copper ring, as shown in the figure. If the magnet is kept fixed while the ring is dropped, what is the direction of the current induced in the ring, as viewed from below the ring?

A conducting rod with a length $\ell = 25 \mathrm {~cm}$ is placed on a U-shaped metal wire that is connected to a lightbulb having a resistance of $8.0 \Omega$ as shown in the figure. The wire and the rod are in the plane of the page. A constant uniform magnetic field of strength $0.40 \mathrm {~T}$ is applied perpendicular to and into the paper. An external applied force moves the rod to the right with a constant speed of $6.0 \mathrm {~m} / \mathrm { s }$ . What are the magnitude and direction of the induced current in the circuit?

A series ac circuit has a resonance frequency of $9.0 \mathrm { kHz }$ . If the inductor in the circuit has a value of $2.0 \mathrm { H }$ , and the resistance is $75 \Omega$ , what is the capacitance of the circuit?

If $V = 40 \mathrm {~V}$ and the battery is ideal, what is the potential difference across $R _ { 1 }$ in the figure?