when the plane of the armature of an a.c. generator is parallel to the field, in which it is rotating,

Options

A. both the flux linked and induced e.m.f in the coil are zero
B. the flux linked with it is zero, while induced e.m.f is maximum
C. flux linked is max. while induced e.m.f is zero
D. both ,the flux and e.m.f have their respective maximum values

Answer

To solve the question regarding the behavior of an AC generator's armature when it is parallel to the magnetic field, we can break down the solution into clear steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- The armature of the AC generator is a coil that rotates in a magnetic field. When we say the armature is parallel to the field, we mean that the plane of the coil is aligned with the direction of the magnetic field.

2. **Identifying the Magnetic Field**:
- Assume the magnetic field (B) is directed into the plane of the paper. The area vector (A) of the coil will be perpendicular to the plane of the coil.

3. **Determining the Angle**:
- When the plane of the armature is parallel to the magnetic field, the angle (θ) between the area vector of the coil and the magnetic field is 90 degrees (θ = 90°).

4. **Calculating Magnetic Flux (Φ)**:
- The magnetic flux (Φ) through the coil is given by the formula:
\[ \Phi = B \cdot A \cdot \cos(\theta) \]
- Substituting θ = 90° into the equation:
\[ \Phi = B \cdot A \cdot \cos(90°) = B \cdot A \cdot 0 = 0 \]
- Therefore, the magnetic flux through the coil is zero when the armature is parallel to the magnetic field.

5. **Induced EMF Calculation**:
- The induced electromotive force (EMF) in the coil can be calculated using Faraday's law of electromagnetic induction:
\[ \text{EMF} = -\frac{d\Phi}{dt} \]
- Since the flux is zero, we need to consider the rate of change of flux. As the coil rotates, the angle changes, and we can express the induced EMF as:
\[ \text{EMF} = -B \cdot A \cdot \frac{d(\cos(\theta))}{dt} \]
- When θ = 90°, the sine function becomes relevant:
\[ \text{EMF} = B \cdot A \cdot \omega \cdot \sin(90°) = B \cdot A \cdot \omega \]
- Here, ω is the angular velocity of the rotating coil. Since sin(90°) = 1, this gives us the maximum induced EMF.

6. **Conclusion**:
- When the plane of the armature of an AC generator is parallel to the magnetic field, the magnetic flux through the coil is zero, and the induced EMF is at its maximum value.

### Final Answer:
- **Magnetic Flux (Φ)**: 0
- **Induced EMF**: Maximum (equal to \(B \cdot A \cdot \omega\))

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