a very thin piece of copper wire has an electrical resistance of 20,000 Ohms. You connect its ends to a regular 2.0 Volt battery. How much power does it draw? Let's assume that this little piece of wire initially contained one trillion (that's a one with 12 zeros) mobile electrons which participate in the electric current flowing through it. How long does it take for an electron that was at one end of the wire when the battery was connected to travel to the other end?
P = V^2/R
Current I = V/R = 10^12* e /Time
(e is the electron charge)
Solve for time t.
To determine the power drawn by the thin copper wire, we can use the formula:
Power (P) = (Voltage (V) ^ 2) / Resistance (R)
Given:
Resistance (R) = 20,000 Ohms
Voltage (V) = 2.0 Volts
Applying the formula:
Power (P) = (2.0^2) / 20,000
Power (P) = 4 / 20,000
= 0.0002 Watts or 0.2 milliwatts
Therefore, the power drawn by the thin copper wire is 0.2 milliwatts.
Now, let's calculate the time it takes for an electron to travel from one end of the wire to the other.
To do this, we need to know the current flowing through the wire. Using Ohm's Law:
Current (I) = Voltage (V) / Resistance (R)
Given:
Voltage (V) = 2.0 Volts
Resistance (R) = 20,000 Ohms
Applying the formula:
Current (I) = 2.0 / 20,000
= 0.0001 Amperes or 100 microamperes
The current is 0.0001 Amperes.
To find the time it takes for an electron to travel from one end of the wire to the other, we need to calculate the total charge passing through the wire.
Charge (Q) = Current (I) * Time (t)
We know that 1 Ampere equals 1 Coulomb of charge passing through a conductor in 1 second. Since we have 0.0001 Amperes of current, each second, 0.0001 Coulombs of charge will pass through the wire.
Now we'll determine the total charge passing through the wire by finding the charge per electron. We're given that there are one trillion (1,000,000,000,000) electrons.
Total Charge = Charge per Electron * Number of Electrons
We need to convert the number of electrons to Coulombs by multiplying by the elementary charge, which is 1.6 * 10^-19 Coulombs.
Total Charge = (0.0001 Coulombs/second) * (1.6 * 10^-19 Coulombs/electron) * (1,000,000,000,000 electrons)
Simplifying the expression:
Total Charge = 1 * 10^-5 Coulombs
Finally, to find the time taken by one electron to travel from one end of the wire to the other, we substitute the values into the equation:
Charge (Q) = Current (I) * Time (t)
1 * 10^-5 = 0.0001 * t
Solving for t:
t = (1 * 10^-5) / 0.0001
t = 0.1 seconds
Therefore, it takes 0.1 seconds for the electron to travel from one end of the wire to the other.