If rotational velocity of a dynamo armature is doubled, then induced e.m.f. will become

Options

A. (a)half
B. (b)two times
C. (c)four times
D. (d)unchanged

Answer

To solve the problem of how the induced electromotive force (e.m.f.) changes when the rotational velocity of a dynamo armature is doubled, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship**: The induced e.m.f. (E) in a dynamo is related to the rotational velocity (ω) of the armature. The relationship can be expressed as:
\[ E \propto \omega \]
This means that the induced e.m.f. is directly proportional to the rotational velocity.

2. **Initial e.m.f.**: Let the initial rotational velocity be denoted as \( \omega_1 \) and the corresponding induced e.m.f. as \( E_1 \). According to the proportionality, we can write:
\[ E_1 = k \cdot \omega_1 \]
where \( k \) is a constant that includes other factors such as the number of turns in the coil, the magnetic field strength, and the area of the coil.

3. **Doubling the rotational velocity**: If the rotational velocity is doubled, we have:
\[ \omega_2 = 2 \cdot \omega_1 \]

4. **Calculate the new e.m.f.**: Using the relationship established, the new induced e.m.f. \( E_2 \) can be expressed as:
\[ E_2 = k \cdot \omega_2 = k \cdot (2 \cdot \omega_1) = 2 \cdot (k \cdot \omega_1) = 2 \cdot E_1 \]

5. **Conclusion**: Thus, when the rotational velocity of the dynamo armature is doubled, the induced e.m.f. becomes:
\[ E_2 = 2 \cdot E_1 \]

### Final Answer:
The induced e.m.f. will become **twice the initial e.m.f.**.