Exam 19: Dc Circuits

What is the magnitude of the potential difference between points $B$ and $C$ for the circuit shown in the figure? The battery is ideal, and all the numbers are accurate to two significant figures.

A $0.200 - \mathrm { H }$ inductor is connected to a $60.0 - \mathrm { Hz } 120 - \mathrm { V }$ rms source. (a) What is the inductive reactance? (b) What is the rms current to the inductor? (c) If both the inductance and the frequency were doubled, what would be the rms current?

A series ac circuit containing a resistor, inductor, and a capacitor has a peak voltage of $116 \mathrm {~V}$ and a peak current of $2.00 \mathrm {~A}$ . If the current lags the voltage by $52.0 ^ { \circ }$ , what is the average power of the circuit?

For the circuit shown in the figure, write the Kirchhoff loop equation for the entire outside loop. Notice the directions of the currents!

In the circuit shown in the figure, all the capacitors are initially uncharged when the switch $\mathrm { S }$ is suddenly closed, and the battery is ideal. Find (a) the maximum reading of the ammeter and (b) the maximum charge on the $5.00 - \mu \mathrm { F }$ capacitor.

A battery has an emf $\varepsilon = 12 \mathrm {~V}$ and an internal resistance $r = 2.0 \Omega$ , as shown in the figure. When a current of $6.0 \mathrm {~A}$ is drawn from the battery, the terminal voltage of the battery $V _ { a b }$ is closest to

As shown in the figure, a circuit consists of a resistor $R = 18 \Omega$ in series with an ideal inductor $L = 33 \mathrm { H }$ having no resistance. At time $t = 0 \mathrm {~s}$ , there is a 12-A current in the circuit. When the magnetic energy of the inductor is $1600 \mathrm {~J}$ , what is the rate of dissipation of energy in the resistor?

A 73-mH solenoid inductor is wound on a form that is $0.80 \mathrm {~m}$ long and $0.10 \mathrm {~m}$ in diameter. A coil having a resistance of $7.7 \Omega$ is tightly wound around the solenoid at its center. The mutual inductance of the coil and solenoid is $19 \mu \mathrm { H }$ . At a given instant, the current in the solenoid is $820 \mathrm {~mA}$ and is decreasing at the rate of $2.5 \mathrm {~A} / \mathrm { s }$ . At the given instant, what is the induced current in the coil?

A $120 - \mathrm { V }$ rms voltage at $1.0 \mathrm { kHz }$ is applied to a $2.0 - \mathrm { mH }$ inductor, a $4.0 - \mu \mathrm { F }$ capacitor and a resistor. If the rms value of the current in this circuit is $0.40 \mathrm {~A}$ , what is the value of the resistor?

A system of four capacitors is connected across a $90 - \mathrm { V }$ voltage source as shown in the figure. What is the equivalent capacitance of this system?

A $120 - \mathrm { V }$ rms voltage at $2000 \mathrm {~Hz}$ is applied to a $6.0 - \mathrm { mH }$ inductor, a $2.0 - \mu \mathrm { F }$ capacitor, and a $200 - \Omega$ resistor. What is the rms value of the current in this circuit?

The peak current and voltage outputs of a generator are 20 A and 240 V, respectively. What average power is provided by the generator?

What resistance is needed in series with a $10 - \mu \mathrm { F }$ capacitor at $1.0 \mathrm { kHz }$ for a total impedance of 45 $\Omega$ ?

A resistor with a resistance of $360 \Omega$ is in a series circuit with a capacitor of capacitance $7.3$ $\times 10 ^ { - 6 } \mathrm {~F}$ . What capacitance must be placed in parallel with the original capacitance to change the capacitive time constant of the combination to three times its original value?

An eagle, with a wingspread of $2.0 \mathrm {~m}$ , flies toward the north at $8.0 \mathrm {~m} / \mathrm { s }$ in a region where the vertical component of the earth's magnetic field is $0.20 \times 10 ^ { - 4 } \mathrm {~T}$ . What emf would be developed between the eagle's wing tips? (It has been speculated that this phenomenon could play a role in the navigation of birds, but the effect is too small, in all likelihood.)

Four resistors are connected across an ideal dc source of $V = 8.0 \mathrm {~V}$ , as shown in the figure. Assume all resistances shown are accurate to two significant figures. What is the current through the $9.0 - \Omega$ resistor?

The network shown is assembled with uncharged capacitors $X , Y$ , and $Z$ , with $C _ { X } = 3.0 \mu F$ , $C _ { Y } = 5.0 \mu \mathrm { F }$ and $\mathrm { C } _ { Z } = 1.0 \mu \mathrm { F }$ . The switches $\mathrm { S } _ { 1 }$ and $\mathrm { S } _ { 2 }$ are initially open, and a potential difference $V _ { a b } = 120 \mathrm {~V}$ is applied between points $a$ and $b$ . After the network is assembled, switch $\mathrm { S } _ { 1 }$ is then closed, but switch $S _ { 2 }$ is kept open. What is the final potential difference across capacitor $Z$ ?

The current through a $50 - \Omega$ resistor is $I = ( 0.80 \mathrm {~A} ) \sin ( 240 t )$ . What are (a) the current amplitude and (b) the rms current?

What is the phase angle between the voltages of the inductor and capacitor in a RLC series circuit?

A $120 - \mathrm { V }$ rms voltage at $60 \mathrm {~Hz}$ is applied across a series combination of a $20 - \mu \mathrm { F }$ capacitor and an unknown resistor. If the rms value of the current in the circuit is $0.60 \mathrm {~A}$ , what is the resistance of the resistor?