The induced emf of a generator when the flux of poles is doubled and speed is doubled

Options

A. becomes half
B. remains same
C. becomes double
D. becomes 4 times

Explanation

To solve the problem of finding the induced emf of a generator when the magnetic flux of the poles is doubled and the speed is doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Formula for Induced EMF**:
The induced electromotive force (emf) in a generator can be expressed as:
\[ E = B \cdot A \cdot \omega \]
where \( E \) is the induced emf, \( B \) is the magnetic flux density, \( A \) is the area of the armature, and \( \omega \) is the angular speed.

2. **Identify Initial Conditions**:
Let the initial magnetic flux be \( \Phi = B \cdot A \) and the initial speed be \( \omega \). Thus, the initial induced emf can be written as:
\[ E_{\text{initial}} = B \cdot A \cdot \omega \]

3. **Apply the Changes**:
According to the problem, both the magnetic flux and the speed are doubled:
- New magnetic flux: \( \Phi' = 2 \Phi = 2B \cdot A \)
- New speed: \( \omega' = 2\omega \)

4. **Calculate the New Induced EMF**:
Substitute the new values into the emf formula:
\[ E_{\text{new}} = \Phi' \cdot \omega' = (2B \cdot A) \cdot (2\omega) \]
Simplifying this gives:
\[ E_{\text{new}} = 4B \cdot A \cdot \omega \]

5. **Relate New EMF to Initial EMF**:
Since \( E_{\text{initial}} = B \cdot A \cdot \omega \), we can express the new emf in terms of the initial emf:
\[ E_{\text{new}} = 4E_{\text{initial}} \]

### Final Answer:
The induced emf of the generator when the flux of the poles is doubled and the speed is doubled is four times the initial induced emf:
\[ E_{\text{new}} = 4E_{\text{initial}} \]