The rectangular coils in a 331 turn generator are 14 cm by 17 cm. What is the maximum emf produced by this generator when it rotates with an angular speed of 525 rpm in a magnetic field of 0.95 T?
To find the maximum emf (electromotive force) produced by the generator, we can use the formula:
emf = NABω
Where:
- emf is the electromotive force (in volts)
- N is the number of turns of the coil
- A is the area of the coil perpendicular to the magnetic field
- B is the magnetic field strength
- ω is the angular speed (in radians per second)
Given:
- N = 331 turns
- A = 14 cm × 17 cm = 238 cm² = 0.0238 m²
- B = 0.95 T
- ω = 525 rpm = 525 × 2π/60 rad/s (converting rpm to rad/s)
Let's calculate the maximum emf step by step:
Step 1: Convert the area from cm² to m²:
A = 0.0238 m²
Step 2: Convert the angular speed from rpm to rad/s:
ω = 525 × 2π/60 rad/s ≈ 55 rad/s
Step 3: Substitute the given values into the formula:
emf = NABω
= (331)(0.0238 m²)(0.95 T)(55 rad/s)
Step 4: Multiply the numbers together:
emf ≈ 428.156 V
Therefore, the maximum emf produced by the generator is approximately 428.156 volts.