Exam 19: Dc Circuits

A fully charged $37 - \mu \mathrm { F }$ capacitor is discharged through a $1.0 - \mathrm { k } \Omega$ resistor. If the voltage across the capacitor is reduced to $7.6$ volts after just $20 \mathrm {~ms}$ , what was the original potential across the capacitor?

What inductance must be put in series with a $200 - \Omega$ resistor at $4.00 \mathrm { kHz }$ to have a total impedance of $240 \Omega$ ?

A $5.0 - \mu \mathrm { F }$ , a $14 - \mu \mathrm { F }$ , and a $21 - \mu \mathrm { F }$ capacitor are connected in series. How much capacitance would a single capacitor need to have to replace the three capacitors?

A $25 - \mathrm { mH }$ inductor is connected in series with a $20 - \Omega$ resistor through an ideal $15 - \mathrm { V }$ dc power supply and a switch. If the switch is closed at time $t = 0 \mathrm {~s}$ , what is the current when $t = 2.0 \mathrm {~ms}$ ?

A $4.0 - \mathrm { mH }$ coil carries a current of $5.0 \mathrm {~A}$ . How much energy is stored in its magnetic field?

A flat circular loop of radius $0.10 \mathrm {~m}$ is rotating in a uniform magnetic field of $0.20 \mathrm {~T}$ . Find the magnetic flux through the loop when the plane of the loop and the magnetic field vector are at an angle of $30 ^ { \circ }$ .

A large electromagnet has a $22 \mathrm {~T}$ magnetic field between its poles. What is the magnetic energy density in that region of space? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

Two 4.0- $\Omega$ resistors are connected in parallel, and this combination is connected in series with $3.0$ $\Omega$ . What is the equivalent resistance of this system?

What is the self-inductance of an ideal solenoid that is $300 \mathrm {~cm}$ long with a cross-sectional area of $1.00 \times 10 ^ { - 4 } \mathrm {~m} ^ { 2 }$ and has 1000 turns of wire? $\left( \mu _ { 0 } = 4 \pi \times 10 ^ { - 7 } \mathrm {~T} \cdot \mathrm { m } / \mathrm { A } \right)$

Determine the current in the $12 - \Omega$ resistor for the circuit shown in the figure assuming that the batteries are ideal.

A galvanometer has an internal resistance of $100 \Omega$ and deflects full-scale at $2.00 \mathrm {~mA}$ . What size resistor should be added to it to convert it to a millivoltmeter capable of reading up to $400 \mathrm { mV }$ ?

A $2.0 - \mu \mathrm { F }$ capacitor is charged to $12 \mathrm {~V}$ and then discharged through a $4.0 - \mathrm { M } \Omega$ resistor. How long will it take for the voltage across the capacitor to drop to $3.0 \mathrm {~V}$ ?

A $1.0 - \mu \mathrm { F }$ capacitor is charged until it acquires a potential difference of $900.0 \mathrm {~V}$ across its plates, and then the emf source is removed. If the capacitor is then discharged through a $500.0 - k \Omega$ resistance, what is the voltage drop across the capacitor $9.0 \mathrm {~ms}$ after beginning the discharge?

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 capacitor as a function of time $t$ ?

Three $2.0 - \Omega$ resistors are connected to form the sides of an equilateral triangle $A B C$ as shown in the figure. What is the equivalent resistance between any two points, $A B , B C$ , or $A C$ , of this circuit?

A round flat metal coil has 180 turns and negligible resistance. It is connected in a series circuit with a 17- $\Omega$ resistor, with nothing else in the circuit. You measure that a $6.0 - \mathrm { A }$ current flows through the resistor when a magnetic field through the coil, perpendicular to its area, is changing at $3.0 \mathrm {~T} / \mathrm { s }$ . What is the radius of the coil?

A flat circular coil having 16 turns, each of diameter 20 cm, is in a uniform and steady 0.13-T magnetic field. (a) Find the total magnetic flux through the coil when the field is perpendicular to the plane of the coil. (b) If the coil is rotated in 10 ms so its plane is parallel to the field, find the average induced emf in the coil.

A airplane having a metal surface and a wingspan of $25.0 \mathrm {~m}$ flies horizontally at $200 \mathrm {~m} / \mathrm { s }$ where the earth's magnetic field is vertical with magnitude $45.0 \mu \mathrm { T }$ . (a) What emf is induced across the wings? (b) What wingspan would the plane need to produce $1.00 - \mathrm { V }$ emf across its wings? (c) The plane now reverses direction. Does the polarity of the wingtip emf change? That is, if the left wing was positive before, does it now become negative?

A flat coil having 40 turns, each one of cross-sectional area 12.0 cm2, is oriented with its plane perpendicular to a uniform magnetic field. The field varies steadily from 0.00 T to 1.20 T in 20.0 ms. What emf is induced in the coil during this time?