Assignment 11: Electrostatics. Electric Current
What is the total surface charge qint on the interior surface of the conductor (i.e., on the wall of the cavity)?
-q
Use the noncontact ammeter to measure the current flowing through the circuit. What is the current?
0.9 A
In a circuit of two lamps in series, where the current through one lamp is 1 A, what is the current through the other lamp? Defend your answer.
1 amp. The same current flows through lamps in series.
How much energy is given to each coulomb of charge that flows through a 1.5-V battery?
1.5 joules
Two conducting spheres are each given a charge Q. The radius of the larger sphere is three times greater than that of the smaller sphere. If the electric field just outside of the smaller sphere is E0, then the electric field just outside of the larger sphere is
1/9 E0 The larger sphere has nine times the surface area of the smaller one, and this reduces the surface charge density by a factor of nine.
How much energy is supplied to each coulomb of charge that flows through a 12-V battery?
12 joules
Which of the figures best represents the charge distribution on the inner and outer walls of the conductor? (Figure 1)
3
What is the current in a bulb if the resistance of its filament is 2 ohms and it is connected across a 6-volt battery?
3 amps
The positive charge is equal to roughly 16 of the smaller charges shown on the surfaces of the spherical shell. Which of the pictures best represents the charge distribution on the inner and outer walls of the shell? (Figure 1)
4
An electric current of 5 amperes in a wire carries _________.
5 coulombs per second
In a circuit of two lamps in parallel, where there is a voltage of 6 V across one lamp, what is the voltage across the other lamp?
6 volts
Consider the power dissipated by the two circuits in the video. The ratio of power dissipation in the parallel circuit to that in the series circuit is
9
What is the voltage reading across the resistor, as shown in the figure below?
9.0 V Since resistance of the wire is essentially zero (an ideal wire), the potential difference between any two locations along the wire is zero. This means that the potential of the end of the resistor with the red probe is equal to the potential of the positive terminal (9 V if the negative terminal is defined to be the zero point of the potential), and the potential of the other end of the resistor is the same as the potential of the negative terminal of the battery. Consequently, voltage across the battery is equal to the magnitude of the voltage drop across the resistor. The results of parts C-H can now be summarized by Ohm's law: I=ΔV/R, where ΔV is the voltage across the resistor.
What condition is necessary for the flow of heat? What analogous condition is necessary for the flow of charge?
A difference in temperature is needed for heat to flow. A difference in electrical potential is needed for charge to flow.
What is a positive ion? What is a negative ion?
A positive ion is a neutral atom that has lost one or more electrons. A negative ion is a neutral atom that has gained one or more electrons.
How does a semiconductor differ from a conductor or an insulator?
A semiconductor is neither a good conductor nor a good insulator - it has a middle range of resistivity.
Between a watt, a kilowatt, and a kilowatt-hour, which is a unit of power and which is a unit of energy?
A watt is power, a kilowatt is power, and a kilowatt-hour is energy.
What is meant by saying that charge is quantized?
All charged objects have a charge that is an integer multiple of the charge of an electron.
How does the charge of one electron compare to that of another electron? How does it compare with the charge of a proton? How do the masses of protons and electrons compare?
All electrons have the same charge. Electron charge is equal and opposite to the proton charge. A proton has 1800 times the mass of an electron.
What kind of charging occurs when you slide your body across a plastic surface?
Charging by friction occurs. Electrons are transferred when one object rubs against another.
What is the relationship between current, resistance, and voltage difference?
Current = Voltage Difference / Resistance
Why are electrons, rather than protons, the principal charge carriers in metal wires?
Electrons are free to move through the metal, whereas protons are fixed in place.
What happens to electrons in any charging process?
Electrons transfer from one place to another.
What is an electric dipole?
In an electric dipole, positive and negative charges are separated on opposite sides of an object.
As in the video, we apply a charge +Q to the half-shell that carries the electroscope. This time, we also apply a charge -Q to the other half-shell. When we bring the two halves together, we observe that the electroscope discharges, just as in the video. What does the electroscope needle do when you separate the two half-shells again?
It does not deflect at all. The spherical surface has zero net charge after the two halves are brought together. The two half-spheres remain electrically neutral after they are separated.
What property of a diode enables it to convert ac to pulsed dc?
It is a one-way valve that allows electrons to in one direction only.
If the resistance of a circuit remains constant while the voltage across the circuit decreases to half its former value, what change occurs in the current?
It is cut to half
What does the power company provide to our homes?
It provides energy to move the electrons.
Why does a wire that carries electric current become hot?
Moving electrons collide with atoms, which transfers their kinetic energy to atomic motion.
How is Coulomb's law similar to Newton's law of gravitation? How is it different?
Newton's law of gravitation is attractive, whereas Coulomb's law is attractive or repulsive. Both are proportional to the inverse square of distance.
What is the relationship among electric power, current, and voltage?
Power is current times voltage.
A voltage source in a circuit provides electrical _________.
Pressure
Using the setup from the first question, imagine that you briefly touch the negatively charged rod to the can. You then hold the two rods at equal distances on either side of the can. What does the can do?
Rolls toward the positively charged rod. The can acquires a net negative charge after being touched, so it is then attracted to the positively charged rod.
Now, consider the situation shown in the figure below. What does the can do?
Stays still The polarization force is always attractive, so the can does not move.
Consider the situation in the figure below, where two charged rods are placed a distance d on either side of an aluminum can. What does the can do?
Stays still The positively charged rod induces a negative charge on the left side of the can, creating an attractive force between the rod and the can. However, the negatively charged rod induces an equal positive charge on the right side of the can, which creates an attractive force between the can and that rod. The net force acting on the can is zero.
How does the flow of current differ in a superconductor compared with the flow in ordinary conductors?
Superconductors have infinite conductivity (current flows forever), whereas ordinary conductors have a small resistance to the flow of electric charge.
What would happen to the two balls if both of them had a non-neutral charge and you slowly increased the mass of the balls?
The angle of the balls with respect to the vertical would decrease.
What would happen to the two balls if one of them were kept positively charged and the charge on the other ball were slowly made increasingly negative?
The balls would begin to move closer together.
What would happen to the two balls if one of them were kept positively charged and the charge on the other ball were slowly increased, making it more and more positive?
The balls would begin to move farther apart.
Does a battery produce dc or ac? Does the generator at a commercial power station produce dc or ac?
The battery is dc; the generator is ac.
When charges mutually repel and distribute themselves on the surface of conductors, what becomes of the electric field inside the conductor?
The charges arrange themselves to make the field inside the conductor zero.
We repeat the experiment from the video, but this time we connect the wires in parallel rather than in series. Which wire will now dissipate the most heat?
The copper wire (resistance 0.1 Ω) The power P dissipated in a wire equals V2/R, where V is the potential difference across the wire and R is the wire's resistance. In a parallel circuit, the potential difference (voltage) is the same across both wires. Therefore, the lower-resistance copper wire dissipates more power and hence is more likely to ignite its paper. In this parallel arrangement we are likely to see both pieces of paper catch fire. Certainly, the copper wire dissipates more heat, but the Nichrome wire will actually dissipate more heat than it did in the series arrangement (can you see why?). Since that was enough to burn the paper in the video, we expect both papers would burn in the parallel arrangement.
Double the resistance of the resistor by changing it from 10 Ω to 20 Ω. What happens to the current flowing through the circuit?
The current decreases by a factor of two. This implies that the current is inversely proportional to the resistance (I∝1/R). You can confirm this by setting the resistance to 30 Ω and measuring the current (it should be one-third of the current for 10 Ω).
How does the current change if you increase the resistance, keeping the voltage difference the same?
The current decreases.
Construct a circuit containing one battery, one resistor, and wire to close the circuit. The order and orientation doesn't matter, but it should look something like the figure below. You can show the values of the components by right-clicking (control-clicking) on each component and selecting Show Value in the pop-up menus. Use the default values of the battery and resistor. You should see the blue electrons flowing through the circuit. In what direction is the current flowing through the circuit? Recall that current is the flow of positive charge.
The current flows from the positive terminal, through the wires and resistor, and into the negative terminal. The electrons flow into the positive terminal; since the electrons are negatively charged, and current is the flow of positive charge, the current is in the opposite direction to the flow of electrons.
For the circuit containing one resistor and one battery, what happens to the current if the voltage is doubled?
The current increases by a factor of two. The current flowing out of the battery is proportional to the voltage of the battery (I∝V). This result, combined with the result of Part D, implies that the current is proportional to the voltage of the battery and inversely proportional to the resistance.
For the circuit containing one resistor and one battery, what happens to the current if the voltage is tripled and the resistance is doubled?
The current increases. Since the current is proportional to the voltage and inversely proportional to the resistance, the current will increase by a factor of 3/2. You can confirm this result with your ammeter.
How is the direction of an electric field defined?
The direction of the field is the direction of the force on a positive test charge.
Why does the gravitational force between Earth and Moon predominate over electrical forces?
The electric force between Earth and Moon cancels out because they have an equal number of positive and negative charges.
What happens to a lamp when you take both ends of the wire connected to it and hold them to the same side of the 12-volt terminal of battery, and why?
The lamp does not light up because there is no voltage difference applied across it.
What happens when you have a voltage difference between the two ends of the lamp, and why?
The lamp lights up because there is a voltage difference applied to it.
A light bulb is basically a resistor that gets so hot that it glows, emitting light. For this tutorial we will assume the resistor in the light bulb is ohmic (that means Ohm's law applies to the resistor). The rate of energy emitted by the light bulb is its output power, commonly referred to as luminosity (brighter means more luminous). Hook up a light bulb to a 5-V battery. Right-click (or control-click) on the light bulb, and change its resistance. How does the brightness of the light bulb depend on its resistance?
The light bulb gets dimmer as the resistance is increased. More current will flow through a light bulb with a lower resistance. The luminosity of the light bulb is equal to the rate at which charges are losing potential energy, so a smaller current produces a smaller luminosity. Note that when you use a dimmer switch in your home, you are controlling the current flowing through the light(s) by adjusting the resistance.
In Part H, you discovered that the luminosity of a light bulb increases if the current increases. The rate at which electric potential energy is converted into heat depends on the current flowing through the bulb and the voltage across the bulb. This energy is supplied by the battery. Mathematically, the luminosity P of the light bulb is given by P=ΔVI, where ΔV is the voltage across the bulb and I is the current. What happens to the luminosity of the light bulb if the voltage of the battery is doubled? (Note that the PhET simulation does not display a numerical value for the luminosity, so you should use the relationship between the luminosity, the voltage across the bulb, and the current.)
The luminosity increases by a factor of four. Both the voltage across the bulb (which is equal to the voltage of the battery) and the current double, so the luminosity increases by a factor of four (since P=ΔVI=(ΔV)2/R). Note that if you took a 100-W light bulb from the U.S. to Europe (where outlets are 240 V rather than 120 V), the luminosity would be 400 W (before breaking)!
Which part of an atom is positively charged, and which part is negatively charged?
The nucleus is positively charged and the electron cloud is negatively charged.
Why are metals good conductors of both heat and electricity?
The outer shell electrons in metals are free to move from atom to atom.
How does the resistance of a thick piece of copper wire compare to the resistance of a thin piece of copper wire?
The resistance of the thin piece is greater than that of the thick piece.
A tipped domino sends a pulse along a row of standing dominoes. Is this a good analogy for the way electric current, sound, or both travel?
This is the way sound travels but not how electric current travels.
What is the primary purpose of a lightning rod?
To prevent a fire caused by lightning
What is the function of fuse or circuit breaker in a circuit?
To prevent over loading the circuit with current
A pipe is filled with water, and there is a piston at each end. If you apply unequal pressures at the two pistons, which way will the water flow in the pipe?
Water will flow from the piston with the higher pressure to the piston with the lower pressure.
How does wetness affect the resistance of your body?
Wet bodies have lower resistance.
Most atoms normally have a net charge that is _________.
Zero
What kind of current runs through the electric wiring in a home?
alternating current
What factors does the resistance offered by a piece of conductor depend upon?
both the geometry and the material of the conductor
When the filament breaks in one lamp in a parallel circuit, lamps in other branches of the circuit normally _________.
continue glowing as brightly
What type of field causes the electrons to do what they do in the wire?
electric field
When your body undergoes electric shock, the source of moving electrons is _________.
electrons already in your body
When you make your household electric payment at the end of the month, are you billed for voltage, current, power, or energy?
energy
Electric power in a circuit is the rate at which _________.
energy dissipates
For the circuit in the previous part, the current flowing in the wire between the positive terminal of the battery and the resistor is ___________ the current flowing between the resistor and the negative terminal of the battery.
equal to The current is the same along the entire circuit. If a greater current were flowing into the resistor than flowing out, charge would have to be building up in the resistor, and this can't happen.
Where do the electrons come from that produce an electric shock when you touch a charged conductor?
inside you
What is the magnitude Eint of the electric field inside the cavity as a function of the distance r from the point charge? Let k, as usual, denote 14πϵ0.
kq/r2
Of what physical quantity is Hertz a unit of?
number of times per second that the electrons move back and forth in the wire
A flow of electric charge in a wire normally requires a _________.
potential difference across the ends of the wire
What is the total surface charge qext on the exterior surface of the conductor?
q
Drag a battery into the construction panel, and use the voltmeter to determine which end of the battery is the positive terminal. The positive terminal has a higher potential than the negative terminal (recall that the voltmeter measures the potential difference between the red probe and the black probe). Which end of the battery is the positive terminal?
the black end Since the positive terminal has a higher potential than the negative terminal, the voltage will be positive if the red probe is placed on the positive terminal and the black probe is placed on the negative probe.
What is the electric field Eext outside the conductor?
the same as the field produced by a point charge q located at the center of the sphere
When we say charge is conserved, we mainly mean that charge can be _________.
transferred without loss like money in a bank
The electric resistance in a length of wire is doubled when the wire is _________.
twice as long
What is the flow of current proportional to?
voltage difference between the two ends of the wire
Electric potential, unlike electric potential energy, is measured in units of _________.
volts
The electric field outside the conductor, Eext:
would change
The electric field within the cavity, Ecav:
would not change
The total surface charge on the exterior of the conductor, qext:
would not change
The total surface charge on the wall of the cavity, qint:
would not change
The net charge on a polarized molecule is normally _________.
zero
The net charge on an energized capacitor is normally _________.
zero
