The resistivity of a certain semi-metal is 10-3 Ohm-cm. Suppose we would like to prepare a silicon wafer with the same resistivi
ty. Assuming we will use n-type dopants only, what dopant density would we choose
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To develop this problem we will apply the concept of energy conservation. For which the work carried out must be equivalent to the potential energy stored on the capacitor. We will start by finding the capacitance to later be able to calculate the energy and therefore the work in the capacitor
Here,
C = Capacitance
V = Potential difference between the plates
Q = Charge between the capacitor plates
At the same time the energy stored in the capacitor can be defined as,
We will start by finding the value of the capacitance, so we will have to,
Finally using the expression for the energy we have that,
Therefore the minimum amount of work that must be done in charging this capacitor is
The work done by the friction force to stop the player is equal to his loss of kinetic energy:
The work done by the friction force is the magnitude of the force
times the distance covered by the player, d:
The loss in kinetic energy is simply equal to the initial kinetic energy of the player, since the final kinetic energy is zero (the player comes to rest):
Substituting into the first equation, we get:
from which we find d, the distance covered by the player:
The work done by the friction force is the magnitude of the force
The loss in kinetic energy is simply equal to the initial kinetic energy of the player, since the final kinetic energy is zero (the player comes to rest):
Substituting into the first equation, we get:
from which we find d, the distance covered by the player: