A 0.35 m2 coil with 50 turns rotates at 5 radians per sec2 in a magnetic field of 0.6 Tesla. What is the value of the rms current in the coil if the coil has the resistance of 3.3 Ù?
Can you also show me how you got the answer? Thanks so much
Apply Faraday's law:
∫B.dS = Φ, dΦ/dt => emf
B = (Bo)sinωt is the sinusoidal magentic flux density.
Flux passing through the coil:
Φ =50(0.35)sin5t=you do it.
Emf = dΦ/dt = 17.5*5cos5t
ω = 5rad/s, f = ω/2π = 5/2π = ...
we need to convert the argument of the sinusoid to degrees
to evaluate the the emf. Use 180/Ï€
Now find max EMF from the expression. Then...
I = V/R = maxEMF/3.3= ...
Instantaneous current:
I = emf/R = (59.2/50)cos377(5) = 0.103 A
you just saved my life
To find the value of the rms current in the coil, we can use the formula:
I = (ε / R),
where I is the current, ε is the induced electromotive force (emf) in the coil, and R is the resistance of the coil.
To find the induced emf, we can use Faraday's law of electromagnetic induction, which states that the induced emf in a coil is equal to the rate of change of magnetic flux through the coil:
ε = -N(dΦ/dt),
where ε is the induced emf, N is the number of turns in the coil, and (dΦ/dt) is the rate of change of magnetic flux.
The magnetic flux through a coil is given by the formula:
Φ = B * A * cos(θ),
where Φ is the magnetic flux, B is the magnetic field, A is the area of the coil, and θ is the angle between the magnetic field and the normal to the coil.
Now, let's plug in the given values:
N = 50 turns,
B = 0.6 Tesla,
A = 0.35 m^2,
θ = 0 degrees (cos(θ) = 1).
First, let's calculate the rate of change of magnetic flux (dΦ/dt):
(dΦ/dt) = B * A * (-sin(θ)) * (dθ/dt).
Since the coil is rotating at a constant angular velocity (5 radians per second), the rate of change of the angle (dθ/dt) is equal to 5 radians per second.
(dΦ/dt) = (0.6 Tesla) * (0.35 m^2) * (-sin(0)) * (5 rad/s).
Since sin(0) = 0, the rate of change of magnetic flux (dΦ/dt) is equal to 0.
Substituting into Faraday's law:
ε = -N(dΦ/dt) = -50 * 0 = 0.
Now, we can calculate the current (I):
I = (ε / R) = 0 / 3.3 Ω = 0 Ampere.
Therefore, the value of the rms current in the coil is 0 Ampere.