A superconductor is a material that has 0 electrical resistance when cooled to below a certain temperature.

In general, materials have a decreasing resistance as they are cooled. With a superconductor, once the critical temperature is reached, the resistance abruptly goes to 0. Superconductivity is a quantum mechanical phenomenon.

We are told that there is an electric field pointing vertically down and that the positive end is near the top. If a charged particle were placed in this field, it will experience an upward electric force, while its mass would cause it to experience a downward gravitational force. We are looking for a situation in which these two forces are equal in order for the particle to be in static equilibrium, thus we need to set the gravitational force equal to the electric force.

To calculate the net charge of the system, it is necessary to know the charge of an electron.  Write the charge of an electron.

Multiply this number by the existing number of electrons in the systems.

For this question, we need to figure out the voltage difference between two points. We're provided with the charge of the particle, the amount of energy put into the process, and the distance traversed by the particle.

First, let's write an equation for voltage.

Where  is electrical potential energy, and  is the charge of the particle.

This equation describes the change in potential energy that occurs when a given quantity of charge undergoes a displacement while within an electric field. Since we are putting energy into this process to make it occur, and the charge is positive, we know that the voltage change will also be positive; that is, the positively charged particle will move towards the positive terminal of a voltage source and away from the negative terminal.

Plugging in the values given to us, we obtain:

Notice that we did not need to know the distance that the particle traveled in this case; that information is extraneous.

Capacitance is directly proportional to area of the parallel plates and indirectly proportional to the distance between the plates. So  and area is doubled  and distance is halved  so the capacitance increases by a factor of 4. 

First, find the total resistance of the circuit. Since the resistors are in parallel, use the following formula:

Plug in known values.

Next, use Ohm's law to find current.

Plug in known values.

Use Ohm's law to find the current passing through each resistor. Because they are in series, they have the same amount of current. Once we get the current, we can plug in the resistance for each resistor to find its potential drop.

Now, find the potential drop across the  resistor.

Therefore, the potential drop across the  resistor is 

Even though there is no resistor, Ohm's law still applies. Use it to find the resistance of the wire.

The resistance of the copper wire is 

First, find the total resistance of the circuit.

 and  are in parallel, so we find the equivalent resistance by using the following formula:

Next, add the series resistors together.

Use Ohm's law to find the current through the system. 

Since  and  are in parallel, they will have the same voltage drop accross them. 

First, find the total resistance of the circuit.

 and  are in parallel, so we find their equivalent resistance by using the following formula:

Next, add the series resistors together.

Use Ohm's law to find the current in the system.

The current through  and  needs to add up to the total current, since they are in parallel.

Also, the voltage drop across them need to be equal, since they are in parallel.

Set up a system of equations.

Solve.