A small canal diverts water from the Perlbach, a river in Bavaria.Water flowing through the canal drops through a small distance andturns a waterwheel, which powers an electric generator, providingelectricity for the house shown in the figure below. (a) Calculate the maximum electrical power thatcan be generated if water moves through the canal at the rate of 1.00 x 10^3 kg/s and drops through a verticaldistance of 2.14 m. (Only about 1 kW isused by the household, the remainder being sold to the local powercompany.) W (b) The generator^'s coil consists of 99turns enclosing an area of 388cm^2. The magnetic field strength is 0.220 T, and the generator operates at 60.0 Hz. Findthe rms value of the emf generated. V (c) Find the maximum rms current through the generator. A
Explanation / Answer
a. Power = workdone / time = potentialenergy / time P = m* g * h / t Given flowof water persecond m/t = 1.00* 103 kg/s height h = 2.14 m P = 1.00* 103 * 9.8 * 2.14 = 2.097* 104 W b. Maximum inducedEMF E0 = * N * B * A here = 2* f = 2* 3.14 * 60 = 376.80 E0 = 376.80* 99 * 0.220 * (388 * 10-4) = 318.42 V RMSvoltage Erms = E0/ 2 = 318.42/ 2 = 225.16 V c. RMScurrent = P / Erms = 2.097* 104 / 225.16 = 93.13 A = 2.097* 104 / 225.16 = 93.13 A