A physics student has a single-occupancy dorm room. The student has a small refrigerator that runs with a current of 3.00 A and a voltage of 110 V, a lamp that contains a 100-W bulb, an overhead light with a 60-W bulb, and various other small devices adding up to 3.00 W. a. Calculate the total current used by the student if all of the devices in their dorm room are operated simultaneously. b. Assume the power plant that supplies electricity to the dorm is 10 km away and uses a single 0-gauge aluminum transmission cable with a diameter of 8.252 mm. Furthermore, initially we will ignore the complications of transformers and assume that the current drawn by the dorm room is also the current on the transmission cable. Calculate the voltage drop across the transmission cable and the minimum voltage that the plant must deliver the electricity so that it is 110 V at the dorm. Hint: treat the transmission cables as cylinders and calculate the cable’s resistance from its length, diameter, and resistivity. c. For the 132 V transmission voltage you found in the previous part, calculate the percentage of electrical power that is lost in transmission.
A physics student has a single-occupancy dorm room. The student has a small refrigerator
that runs with a current of 3.00 A and a voltage of 110 V, a lamp that contains a 100-W bulb,
an overhead light with a 60-W bulb, and various other small devices adding up to 3.00 W.
a. Calculate the total current used by the student if all of the devices in their dorm
room are operated simultaneously.
b. Assume the power plant that supplies electricity to the dorm is 10 km away and uses
a single 0-gauge aluminum transmission cable with a diameter of 8.252 mm.
Furthermore, initially we will ignore the complications of transformers and assume
that the current drawn by the dorm room is also the current on the transmission
cable. Calculate the voltage drop across the transmission cable and the minimum
voltage that the plant must deliver the electricity so that it is 110 V at the dorm.
Hint: treat the transmission cables as cylinders and calculate the cable’s resistance
from its length, diameter, and resistivity.
c. For the 132 V transmission voltage you found in the previous part, calculate the
percentage of electrical power that is lost in transmission.
d. What would be the percentage of power lost if the power company used
transformers to deliver the electric power at 110 kV? Hint: The transmission current
will be much smaller now and can be calculated using P=IV.
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