power station generates 250kW of power at a potential difference of 25kV. Theenergy is transmitted through cables of total resistance 4.0Ω.What is the power loss in the cables?
Question
power station generates 250kW of power at a potential difference of 25kV. Theenergy is transmitted through cables of total resistance 4.0Ω.What is the power loss in the cables?
Solution
To solve this problem, we first need to find the current flowing through the cables. We can use Ohm's law for this, which states that the current (I) is equal to the voltage (V) divided by the resistance (R).
Step 1: Convert the voltage from kV to V: 25kV = 25000V
Step 2: Calculate the current using Ohm's law: I = V/R = 25000V / 4.0Ω = 6250A
Next, we need to find the power loss in the cables. The power loss can be calculated using the formula P = I^2R, where P is the power loss, I is the current, and R is the resistance.
Step 3: Calculate the power loss: P = I^2R = (6250A)^2 * 4.0Ω = 156250000W = 156250kW
So, the power loss in the cables is 156250kW.
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