In an AC generator, a coil with N turns, all of the same area A and total resistance R, rotates with frequency `(omega)` in a magnetic field B. The maximum value of emf generated in the coils is

Options

A. `N.A.B.R.omega`
B. `N.A.B`
C. `N.A.B.R`
D. `N.A.B.omega`

Explanation

To find the maximum value of the electromotive force (emf) generated in an AC generator, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Components**:
- The AC generator consists of a coil with \( N \) turns, area \( A \), total resistance \( R \), rotating in a magnetic field \( B \) with angular frequency \( \omega \).

2. **Induced EMF Formula**:
- The induced emf (\( E \)) in the coil can be derived from Faraday's law of electromagnetic induction, which states:
\[ E = -\frac{d\Phi}{dt} \]
where \( \Phi \) is the magnetic flux.

3. **Magnetic Flux Calculation**:
- The magnetic flux (\( \Phi \)) through one turn of the coil is given by:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
where \( \theta \) is the angle between the magnetic field and the normal to the coil's surface. As the coil rotates, \( \theta \) changes with time, and we can express it as:
\[ \theta = \omega t \]
Thus, the magnetic flux becomes:
\[ \Phi = B \cdot A \cdot \cos(\omega t) \]

4. **Differentiating the Flux**:
- To find the induced emf, we differentiate the magnetic flux with respect to time:
\[ \frac{d\Phi}{dt} = \frac{d}{dt}(B \cdot A \cdot \cos(\omega t)) = -B \cdot A \cdot \omega \sin(\omega t) \]
- Therefore, the induced emf is:
\[ E = -N \frac{d\Phi}{dt} = -N \left(-B \cdot A \cdot \omega \sin(\omega t)\right) = N B A \omega \sin(\omega t) \]

5. **Finding Maximum EMF**:
- The maximum value of the induced emf occurs when \( \sin(\omega t) \) is at its maximum value, which is 1. This occurs when \( \omega t = \frac{\pi}{2} \) (or 90 degrees).
- Thus, the maximum emf (\( E_{\text{max}} \)) is given by:
\[ E_{\text{max}} = N B A \omega \]

### Final Answer:
The maximum value of the emf generated in the coils is:
\[ E_{\text{max}} = N B A \omega \]