Generator Physics Example 4

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Example 4

hard
A hydroelectric generator produces 10 MW10 \text{ MW} at 20,000 V20{,}000 \text{ V} RMS. What RMS current does it deliver? If the transmission line has 2 Ω2 \text{ } \Omega resistance, what percentage of power is lost in transmission?

Solution

  1. 1
    RMS current: I=PV=10×10620,000=500 AI = \frac{P}{V} = \frac{10 \times 10^6}{20{,}000} = 500 \text{ A}.
  2. 2
    Power lost in transmission: Ploss=I2R=5002×2=500,000 W=0.5 MWP_{\text{loss}} = I^2 R = 500^2 \times 2 = 500{,}000 \text{ W} = 0.5 \text{ MW}.
  3. 3
    Percentage lost: 0.510×100%=5%\frac{0.5}{10} \times 100\% = 5\%.

Answer

I=500 A,Ploss=5%I = 500 \text{ A}, \quad P_{\text{loss}} = 5\%
Transmission losses depend on the square of the current. This is why power is transmitted at high voltages — it reduces the current and therefore the I2RI^2R losses in the wires.

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A device that converts mechanical (kinetic) energy into electrical energy by rotating a coil of wire within a magnetic field, exploiting electromagnetic induction.

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