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
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.