The maximum value of the emf generated in a 32 turn coil is 260V. The coil with dimensions of 360mm by 200mm is rotated by an axis by an axis through the centre and parallel to the coil sides. Calculate the following if the field has a uniform magnetic flux density of 0,86T:
a) The speed at which the coil is rotated
b) the instantaneous value of the emf 90° after reaching the maximum
c) the instantaneous value of the emf 20° before reaching the maximum
a) To calculate the speed at which the coil is rotated, we need to use the equation for the induced electromotive force (emf) in a rotating coil:
emf = N * B * A * ω
Where:
emf is the induced emf (260V in this case)
N is the number of turns in the coil (32 turns)
B is the magnetic flux density (0.86T)
A is the area of the coil (length * width = 360mm * 200mm = 72000 mm² = 0.072m²)
ω is the angular velocity (in radians per second)
Rearranging the equation, we can solve for ω:
ω = emf / (N * B * A)
Substituting the given values:
ω = 260 / (32 * 0.86 * 0.072)
Calculating the value gives:
ω ≈ 138.16 rad/s
Therefore, the speed at which the coil is rotated is approximately 138.16 radians per second.
b) To find the instantaneous value of the emf 90° after reaching the maximum, we can use the equation for the emf in a rotating coil:
emf = N * B * A * ω * sin(θ)
Where θ is the angle between the coil's normal vector and the magnetic field vector.
90° after reaching the maximum, θ would be 90°.
emf = 32 * 0.86 * 0.072 * 138.16 * sin(90°)
Calculating the value gives:
emf ≈ 263.21V
Therefore, the instantaneous value of the emf 90° after reaching the maximum is approximately 263.21V.
c) To find the instantaneous value of the emf 20° before reaching the maximum, we can use the same equation as in part b:
emf = N * B * A * ω * sin(θ)
Where θ is the angle between the coil's normal vector and the magnetic field vector.
20° before reaching the maximum, θ would be 70°.
emf = 32 * 0.86 * 0.072 * 138.16 * sin(70°)
Calculating the value gives:
emf ≈ 216.45V
Therefore, the instantaneous value of the emf 20° before reaching the maximum is approximately 216.45V.