The LRT trolley system 10 miles long is fed by two substations that generate 600 volts and 560 volts, respectively. the resistance of the trolley wire and rail return is 0.3 ohm per mile. if the car located 4 miles from the 600-volt station draws 200A from the line, how much is the current supplied by each station?
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To determine the current supplied by each station, we need to calculate the voltage drop along the trolley wire and rail return.
First, we calculate the total voltage drop:
Voltage drop = (Resistance per mile) x (Distance between the car and the 600-volt station)
Voltage drop = 0.3 ohm/mile x 4 miles
Voltage drop = 1.2 volts
Next, we calculate the voltage at the car's location:
Voltage at the car's location = Voltage supplied by the 600-volt station - Voltage drop
Voltage at the car's location = 600 volts - 1.2 volts
Voltage at the car's location = 598.8 volts
Now, we can determine the current supplied by each station using the voltage and resistance:
For the 600-volt station:
Current = Voltage / Resistance
Current = 598.8 volts / 0.3 ohm/mile x 10 miles
Current = 598.8 volts / 3 ohms
Current = 199.6 amperes
For the 560-volt station:
Current = Voltage / Resistance
Current = 560 volts / 0.3 ohm/mile x 10 miles
Current = 560 volts / 3 ohms
Current = 186.7 amperes
Therefore, the current supplied by the 600-volt station is approximately 199.6 amperes, and the current supplied by the 560-volt station is approximately 186.7 amperes.
To determine the current supplied by each station, we can use Ohm's Law, which states that current (I) is equal to voltage (V) divided by resistance (R).
First, let's calculate the total resistance of the trolley wire and rail return for the given distance of 10 miles. The resistance per mile is given as 0.3 ohms, so the total resistance (RTotal) is:
RTotal = Resistance Per Mile x Total Distance
RTotal = 0.3 ohm/mile x 10 miles
RTotal = 3 ohms
Next, we need to determine the voltage drop across the 4 miles of wire between the car and the 600-volt station. This can be calculated using Ohm's Law:
Voltage Drop (VDrop) = Current (I) x Resistance (R)
VDrop = 200A x (0.3 ohm/mile x 4 miles)
VDrop = 200A x 1.2 ohms
VDrop = 240 volts
Now that we know the voltage drop across the 4 miles of wire to the car is 240 volts, we can subtract this from the 600-volt supply to find the voltage at the car:
Voltage at Car = Supply Voltage - Voltage Drop
Voltage at Car = 600 volts - 240 volts
Voltage at Car = 360 volts
Finally, to calculate the current supplied by each station, we can divide the voltage at the car by the respective substation voltages:
Current from 600-volt Station = Voltage at Car / Substation Voltage
Current from 600-volt Station = 360 volts / 600 volts
Current from 600-volt Station = 0.6 or 600 Amps
Similarly,
Current from 560-volt Station = Voltage at Car / Substation Voltage
Current from 560-volt Station = 360 volts / 560 volts
Current from 560-volt Station = 0.643 or 643 Amps
Therefore, the 600-volt station supplies 600 Amps, while the 560-volt station supplies 643 Amps.