Final answer:
The number of turns needed in the generator coil can be calculated using Faraday's Law of Induction and the known values for peak emf, coil dimensions, magnetic field strength, and frequency. By rearranging the formula for induced emf, we can solve for the number of turns, which is essential in designing a generator to meet specific voltage and frequency requirements.
Step-by-step explanation:
To calculate the number of turns needed in the coil of a generator to produce a peak value of 6.7 kV alternating emf at 60 Hz, we use Faraday's Law of Induction, which states that the induced emf (ε) in a coil is equal to the rate of change of the magnetic flux through the coil. The peak emf (ε_max) can be expressed by the formula ε_max = NABωsin(ωt), where N is the number of turns in the coil, A is the area of the coil, B is the magnetic field strength, and ω is the angular velocity of the coil.
The area (A) can be calculated by multiplying the length and width of the coil. In this case, A = 70 cm * 120 cm = 0.7 m * 1.2 m = 0.84 m². The angular frequency (ω) for a 60 Hz AC generator is ω = 2πf = 2π * 60 Hz = 120π rad/s.
Therefore, since ε_max is given as 6.7 kV, we can rearrange the formula to solve for N: N = ε_max / (ABω). Plugging in the known values, we have N = 6700 V / (0.84 m² * 0.15 T * 120π rad/s). Simplifying this expression gives us the number of turns required. The precise calculations should be performed to find the exact value for N, ensuring that the generator produces the desired peak emf of 6.7 kV at 60 Hz.