An average of 120KW of electric power is sent to a small town from a power plant constant 10km away.the transmission lines have a total resistance of 0.4ohms, calculate the power loss if the is transmitted at 240v.
E*I = 120,000 W.
240I = 120,000,
I = 500A.
P = I^2 * R = 500^2 * 0.4 = 100,000W = 100 kW. = power lost.
To calculate the power loss in the transmission lines, we need to use the formula:
Power loss = (I^2) * R
Where,
I = Current flowing through the transmission lines
R = Total resistance of the transmission lines
To find the current flowing through the transmission lines, we can use Ohm's Law:
I = V / R
Where,
V = Voltage
Given:
Total resistance (R) of the transmission lines = 0.4 ohms
Voltage (V) = 240 volts
Substituting the values into Ohm's Law, we can calculate the current:
I = 240 / 0.4
I = 600 Amperes
Now, we can calculate the power loss:
Power loss = (I^2) * R
Power loss = (600^2) * 0.4
Calculating the power loss:
Power loss = 360,000 * 0.4
Power loss = 144,000 Watt
Therefore, the power loss in the transmission lines is 144,000 Watts or 144 kW.
To calculate the power loss in the transmission lines, we can use the formula:
Power loss = (I^2) * R
Where:
I = Current (in Amperes)
R = Resistance (in Ohms)
First, let's calculate the current flowing through the transmission lines. We know that power (P) is equal to voltage (V) multiplied by current (I):
P = V * I
Rearranging the formula, we can isolate the current (I):
I = P / V
Substituting the given values into the formula, we have:
I = 120,000 W / 240 V
I = 500 A
Now that we have the current, we can calculate the power loss using the formula:
Power loss = (I^2) * R
Substituting the values:
Power loss = (500 A)^2 * 0.4 Ω
Power loss = 250,000 * 0.4
Power loss = 100,000 W
Therefore, the power loss in the transmission lines is 100,000 Watts.
i^2 R
where
i = V/R = 240/0.4