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
d) the instantaneous value of the emf 20° before reaching the maximum
a) To calculate the speed at which the coil is rotated, we can use the formula for emf induced in a rotating coil:
emf = NABω
Where emf is the electromagnetic force induced in the coil, N is the number of turns in the coil, A is the area of the coil, B is the magnetic flux density, and ω is the angular velocity.
Given:
emf = 260 V
N = 32 turns
A = (360 mm) * (200 mm) = 72,000 mm^2 = 0.072 m^2
B = 0.86 T
We can rearrange the formula to solve for ω:
ω = emf / (NAB)
ω = 260 V / (32 * 0.072 m^2 * 0.86 T)
ω ≈ 128.11 rad/s
So, the speed at which the coil is rotated is approximately 128.11 rad/s.
b) To calculate the instantaneous value of the emf 90° after reaching the maximum, we can use the formula:
emf = NABωsinθ
Where θ is the angle between the normal to the coil and the magnetic field.
Given:
θ = 90°
emf = 32 * 0.072 m^2 * 0.86 T * 128.11 rad/s * sin(90°)
emf ≈ 291.94 V
So, the instantaneous value of the emf 90° after reaching the maximum is approximately 291.94 V.
d) To calculate the instantaneous value of the emf 20° before reaching the maximum, we use the same formula as above:
θ = -20°
emf = 32 * 0.072 m^2 * 0.86 T * 128.11 rad/s * sin(-20°)
emf ≈ -91.98 V
So, the instantaneous value of the emf 20° before reaching the maximum is approximately -91.98 V.