If the speed of rotation of a dynamo is doubled, then the induced emf will :

Options

A. become four times
B. become half
C. remain unchanged
D. become double

Answer

To solve the question regarding the effect of doubling the speed of rotation of a dynamo on the induced electromotive force (emf), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Formula for Induced EMF**:
The induced emf (E) in a dynamo can be expressed by the formula:
\[ E = NAB\omega \sin(\theta) \]
where:
- \(N\) = number of turns in the coil
- \(A\) = area of the coil
- \(B\) = magnetic field strength
- \(\omega\) = angular velocity (speed of rotation)
- \(\theta\) = angle between the magnetic field and the normal to the coil's surface

2. **Identifying Constants**:
In this scenario, \(N\), \(A\), and \(B\) are constants for a given dynamo. The only variable that we are changing is \(\omega\), the angular velocity.

3. **Doubling the Speed of Rotation**:
If the speed of rotation is doubled, then:
\[ \omega' = 2\omega \]
where \(\omega'\) is the new angular velocity.

4. **Substituting into the EMF Formula**:
Substitute \(\omega' = 2\omega\) into the induced emf formula:
\[ E' = NAB(2\omega) \sin(\theta) \]
This simplifies to:
\[ E' = 2NAB\omega \sin(\theta) \]
Therefore, we can see that:
\[ E' = 2E \]
where \(E\) is the original induced emf.

5. **Conclusion**:
The induced emf will be double the original value when the speed of rotation of the dynamo is doubled.

### Final Answer:
The induced emf will become double.