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 Ω?
To find the value of the rms current in the coil, we need to use the formula relating the current, magnetic field, number of turns, and area of the coil.
The formula for the EMF (Electromotive Force) induced in a rotating coil is given by:
EMF = NABω
Where:
EMF is the electromotive force (voltage) induced in the coil,
N is the number of turns in the coil,
A is the area of the coil,
B is the magnetic field strength, and
ω is the angular speed of rotation.
In this case, the area of the coil A is given as 0.35 m^2, the number of turns N is 50, the angular speed ω is 5 radians per second, and the magnetic field strength B is 0.6 Tesla.
Plugging in these values into the formula, we get:
EMF = (50)(0.35)(0.6)(5) = 52.5 volts
The next step is to use Ohm's Law, which states that the current (I) in a circuit is equal to the voltage (V) divided by the resistance (R). In this case, the resistance (R) is given as 3.3 Ω. Therefore:
I = V / R = 52.5 / 3.3 ≈ 15.91 amps
So, the value of the rms current in the coil is approximately 15.91 amps.