The coil in an A.c generator consists of 8 turns of wire, each of area A=0.090m², and the total resistance of the wire is 12.0ohms. The coil rotates in a 0.500T magnetic field at a constant frequency of 60.0Hz. Find the maximum induced emf in the coil

Answer 1

The maximum induced emf in the coil can be calculated using the formula:

Emax = NΔΦ/Δt

where:
N = number of turns of wire = 8
ΔΦ = change in magnetic flux
Δt = change in time

To calculate ΔΦ, we can use the formula:

ΔΦ = BΔA

where:
B = magnetic field strength = 0.500 T
ΔA = change in area = A (since the area is constant)

Substituting the given values:

ΔΦ = (0.500 T)(0.090 m²) = 0.045 Wb

Next, we need to calculate Δt. Since the frequency is given as 60.0 Hz, the period (T) can be calculated as:

T = 1/f = 1/60 Hz = 0.0167 s

The change in time (Δt) for one complete cycle is equal to the period:

Δt = 0.0167 s

Now, we can substitute the values into the first formula to calculate the maximum induced emf:

Emax = NΔΦ/Δt
= (8 turns)(0.045 Wb)/(0.0167 s)
= 0.216 V

Therefore, the maximum induced emf in the coil is 0.216 V.