Hi! Need help please, thank you.
Question:In a model AC generator, a 498 turn rectangular coil 14.0 cm by 21 cm rotates at 124 rev/min in a uniform magnetic field of 0.65 T.
(a) What is the maximum emf induced in the coil?
___ V
(b) What is the instantaneous value of the emf in the coil at t = (ð/30) s? Assume that the emf is zero at t = 0.
____V
(c) What is the smallest value of t for which the emf will have its maximum value?
____
The correct answer is not zero. s
To find the answers to these questions, we need to use the formula for the induced electromotive force (emf) in an AC generator:
EMF = NBAωsin(θ)
Where:
EMF is the induced electromotive force
N is the number of turns in the coil
B is the magnetic field strength
A is the area of the coil
ω is the angular velocity (in radians per second)
θ is the angle between the magnetic field and the normal to the coil
Now, let's solve each part of the question step by step.
(a) What is the maximum emf induced in the coil?
To find the maximum emf, we need to calculate the maximum value of sin(θ). In this case, the maximum value of sin(θ) is 1 when the angle θ is 90 degrees or π/2 radians.
Given:
N = 498 turns
B = 0.65 T
A = 14.0 cm * 21 cm = 294 cm^2 = 0.0294 m^2
ω = 124 rev/min = 124 * 2π rad/min = (124 * 2π) / 60 rad/s
Using the formula for EMF, we can now substitute these values:
EMF = (N * B * A * ω * sin(θ)) max
= (498 * 0.65 * 0.0294 * (124 * 2π / 60) * 1)
Solving this equation will give us the maximum emf in volts.
(b) What is the instantaneous value of the emf in the coil at t = (π/30) s? Assume that the emf is zero at t = 0.
To find the instantaneous value of the emf at a specific time, we need to calculate sin(θ) for that time. This can be done by using the formula:
θ = ωt
Given the value of t = (π/30) s, we can substitute it into the equation:
θ = (124 * 2π / 60) * (π/30)
Using the value of θ, we can substitute it into the formula for EMF:
EMF = (N * B * A * ω * sin(θ))
Solving this equation will give us the instantaneous value of the emf at t = (π/30) s.
(c) What is the smallest value of t for which the emf will have its maximum value?
The maximum value of the emf occurs when sin(θ) is 1. Since sin(θ) = 1 when θ = π/2, we can calculate the value of t that corresponds to this angle using the equation:
θ = ωt
By rearranging the equation, we can solve for t:
t = θ / ω
Substituting θ = π/2 and the given value of ω, we can find the smallest value of t for which the emf will have its maximum value.