Q:A 50 turns coil in a generator has an area 500cm(square)rotates in magnetic field with B=1.76 w/m(square), how fast must the coil be rotated in order to generate a maximum voltage of 220 volt?
PLZ EXPLAIN WITH DATA!
To find out how fast the coil must be rotated in order to generate a maximum voltage of 220 volts, we can use Faraday's Law of Electromagnetic Induction.
Faraday's Law states that the electromotive force (EMF) induced in a conducting loop is directly proportional to the rate of change of magnetic flux passing through the loop. Mathematically, it is represented as:
EMF = -N * dΦ/dt
Where:
EMF is the electromotive force or voltage induced (in volts)
N is the number of turns in the coil
dΦ/dt is the rate of change of magnetic flux (in webers per second)
First, let's calculate the magnetic flux (Φ) passing through the coil. The magnetic flux is given by the equation:
Φ = B * A
Where:
B is the magnetic field strength (in webers per square meter)
A is the area of the coil (in square meters)
In this case, the values given are:
B = 1.76 Wb/m²
A = 500 cm² = 500 / 10000 = 0.05 m²
Substituting these values into the equation, we can calculate the magnetic flux:
Φ = (1.76 Wb/m²) * (0.05 m²)
Φ = 0.088 Wb
Now, we can substitute the calculated magnetic flux (Φ) and the desired maximum voltage (220 volts) into the equation for EMF:
EMF = -N * dΦ/dt
Since we want to find the rate of change of magnetic flux (dΦ/dt) required to generate a maximum voltage of 220 volts, we rearrange the equation:
dΦ/dt = EMF / -N
Substituting the values, we get:
dΦ/dt = 220 V / -N
The number of turns in the coil is given as 50 turns, so we substitute N = 50 into the equation:
dΦ/dt = 220 V / -(50 turns)
Now, we have the rate of change of magnetic flux required to generate a maximum voltage of 220 volts. This value represents how fast the coil must be rotated.
Please note that the units used in the calculations are consistent and ensure dimensional accuracy.
http://en.wikipedia.org/wiki/Electromagnetic_induction
Flux is 500cm^2 (change that to m^2)times B times winding turns. deltatime is the reciprocal of frequency.
emf=- d flux/dt= -Area*B*n/time=-area*B*rate*n
solve for rate.