A generator has a square coil consisting of 700 turns. The coil rotates at 78 rad/s in a 0.21-T magnetic field. The peak output of the generator is 120.00 V. What is the length of one side of the coil?
To find the length of one side of the coil, we can use the formula:
Emf (ε) = N * B * A * ω
Where:
ε = emf (electromotive force)
N = number of turns in the coil
B = magnetic field strength
A = area of the coil
ω = angular velocity of the coil
Given:
N = 700 turns
B = 0.21 T
ε = 120 V
ω = 78 rad/s
We can rearrange the formula to solve for A:
A = ε / (N * B * ω)
Substituting the given values:
A = 120 V / (700 turns * 0.21 T * 78 rad/s)
Calculating the value:
A ≈ 0.003927 m^2
Since the coil is square-shaped, the area is equal to the length of one side squared. Therefore:
Length of one side of the coil = √A
Length of one side of the coil = √(0.003927 m^2)
Length of one side of the coil ≈ 0.063 m
So, the length of one side of the coil is approximately 0.063 meters.
To find the length of one side of the coil, we can use the formula:
EMF = N * B * A * ω
where:
- EMF is the electromotive force (peak output of the generator in volts)
- N is the number of turns in the coil
- B is the magnetic field strength in teslas
- A is the area of the coil in square meters
- ω (omega) is the angular velocity of the coil in radians per second
We are given:
- EMF = 120.00 V
- N = 700
- B = 0.21 T
- ω = 78 rad/s
Rearranging the formula, we have:
A = EMF / (N * B * ω)
Plugging in the given values, we get:
A = 120.00 V / (700 turns * 0.21 T * 78 rad/s)
Now, let's calculate the value of A.