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 (Electromotive force) = N * B * A * ω

Where:
EMF is the peak output voltage of the generator (120.00 V),
N is the number of turns in the coil (700 turns),
B is the magnetic field strength (0.21 T),
A is the area of the coil, and
ω is the angular velocity of rotation (78 rad/s).

We can rearrange the formula to solve for A:

A = EMF / (N * B * ω)

Now let's plug in the given values to calculate A:

A = 120.00 V / (700 turns * 0.21 T * 78 rad/s)

By performing the calculation, we get:

A ≈ 0.0061 m^2

Since we have a square coil, we can calculate the length of one side by taking the square root of the area:

Length of one side = √(A)

Thus,

Length of one side ≈ √(0.0061 m^2)

By evaluating the square root, we find:

Length of one side ≈ 0.078 m

Therefore, the length of one side of the coil is approximately 0.078 meters.