In a 220-turn automobile alternator, the magnetic flux in each turn is 2.50x10^(-2) T, where T is in webers, ω is the angular speed of the alternator, and t is in seconds. The alternator is geared to rotate six times for each engine revolution. The engine is running at an angular speed of 1.00x10^(2) rev/min.
(a) Determine the induced emf in the alternator as a function of time. (Assume ω is in V.) The induced emf can be calculated using the formula: emf = N * dϕ/dt, where N is the number of turns and dϕ/dt is the rate of change of magnetic flux. In this case, N = 220 and dϕ/dt = 2.50x10^(-2) * ω. Therefore, the induced emf is 220 * 2.50x10^(-2) * ω.
(b) Determine the maximum emf in the alternator. The maximum emf can be calculated by substituting the maximum value of ω into the formula from part (a). The maximum value of ω can be found by converting the angular speed of the engine from rev/min to rad/s. The conversion factor is 2π/60. Therefore, the maximum value of ω is 1.00x10^(2) * 2π/60. Substituting this value into the formula, the maximum emf is 220 * 2.50x10^(-2) * (1.00x10^(2) * 2π/60).
What are the maximum values of the sine and cosine functions? The maximum value of the sine function is 1, and the maximum value of the cosine function is also 1.