An emf is generated by an ac generator having 100 turn coil, of loop area 1 m². The coil rotates at a speed of

Question

An emf is generated by an ac generator having 100 turn coil, of loop area 1 m². The coil rotates at a speed of one revolution per second and placed in a uniform magnetic field of 0.05 T perpendicular to the axis of rotation of the coil. The maximum value of emf is:

Accepted Answer

The maximum electromotive force ($\varepsilon_{max}$) generated in an AC generator is given by the formula:
$$\varepsilon_{max} = NBA\omega$$

**1. Identify Given Values:**
*   Number of turns ($N$) = 100
*   Area of the coil ($A$) = $1 	ext{ m}^2$
*   Magnetic Field Strength ($B$) = $0.05 	ext{ T}$
*   Frequency of rotation ($
u$) = $1 	ext{ revolution per second} = 1 	ext{ Hz}$

**2. Calculate Angular Velocity ($\omega$):**
$$\omega = 2\pi
u = 2\pi(1) = 2\pi 	ext{ rad/s}$$

**3. Calculate Maximum EMF:**
Substituting the values into the formula:
$$\varepsilon_{max} = 100 	imes 0.05 	imes 1 	imes 2\pi$$
$$\varepsilon_{max} = 5 	imes 2\pi$$
$$\varepsilon_{max} = 10\pi$$

Using the approximation $\pi \approx 3.14$:
$$\varepsilon_{max} = 10 	imes 3.14 = 31.4 	ext{ V}$$

Step-by-Step Solution

Practice All PHYSICS Questions