In a hydroelectric installation, a turbine delivers 1500 hp to a generator, which in turn transfers 80.0% of the mechanical energy out by electrical transmission. Under these conditions, what current does the generator deliver at a terminal potential difference of 1910 V?
There are a few different horsepower definitions - imperial, metric, DIN etc but an average conversion factor is 1hp = 745W
Generator input = 1500 * 745 W = 1117500W
Generator output = 1117500W * 80.0% = 894000W (3 sig figs)
Current = 894000W / 1910V = 468.06A
To find the current delivered by the generator, we can use the formula:
Power (P) = Voltage (V) × Current (I)
Given:
Power delivered to the generator (P) = 1500 hp
Efficiency of the generator (η) = 80.0% = 0.80
Terminal potential difference (V) = 1910 V
First, we need to convert the power from horsepower (hp) to watts (W) since the formula requires power in watts. We know that 1 hp is equal to 746 W.
Power (P) = 1500 hp × 746 W/hp = 1,119,000 W
Next, we need to calculate the mechanical power supplied to the generator using the efficiency of the generator:
Mechanical power (Pm) = Power (P) / Efficiency (η)
Pm = 1,119,000 W / 0.80 = 1,398,750 W
Now that we have the mechanical power, we can use the formula to find the current:
Current (I) = Power (Pm) / Voltage (V)
I = 1,398,750 W / 1910 V = 732.51 A
Therefore, the generator delivers a current of approximately 732.51 A at a terminal potential difference of 1910 V.
To find the current delivered by the generator, we can use the formula:
Power (P) = Voltage (V) × Current (I)
We're given:
Power delivered to the generator = 1500 hp
Efficiency of electrical transmission = 80.0% = 0.80
Terminal potential difference = 1910 V
First, let's convert the power in horsepower to watts. We know that 1 horsepower is equal to 746 watts.
Power (in watts) = 1500 hp × 746 watts/hp = 1,119,000 watts
Next, we need to find the electrical power output of the generator. Since the generator transfers only 80% of the mechanical energy as electrical power, we'll multiply the mechanical power by the efficiency.
Electrical power output = Power × Efficiency = 1,119,000 watts × 0.80 = 895,200 watts
Now, we can rearrange the formula to solve for current:
Current (I) = Power (P) / Voltage (V)
Substituting the values we have:
Current (I) = 895,200 watts / 1910 V
Calculating this, we find:
Current (I) = 469.16 A
Therefore, the generator delivers a current of approximately 469.16 Amperes.