The induced e.m.f. in a coil does not depend on

Options

A. The number of turns in the coil
B. The rate of change of magnetic flux
C. Time of rotation
D. The resistance of the circuit

Answer

To determine what the induced electromotive force (e.m.f.) in a coil does not depend on, we can analyze the factors that influence induced e.m.f. based on Faraday's law of electromagnetic induction.

### Step-by-Step Solution:

1. **Understanding Induced EMF**:
According to Faraday's law, the induced e.m.f. (ε) in a coil is given by the formula:
\[ \varepsilon = -\frac{d\Phi_B}{dt} \]
where \(\Phi_B\) is the magnetic flux through the coil.

2. **Magnetic Flux**:
The magnetic flux (\(\Phi_B\)) is defined as:
\[ \Phi_B = B \cdot A \cdot \cos(\theta) \]
where:
- \(B\) is the magnetic field strength,
- \(A\) is the area of the coil,
- \(\theta\) is the angle between the magnetic field and the normal to the surface of the coil.

3. **Factors Affecting Induced EMF**:
The induced e.m.f. depends on:
- The rate of change of magnetic flux (\(d\Phi_B/dt\)).
- The number of turns in the coil (more turns lead to more induced e.m.f.).
- The area of the coil (larger area can capture more magnetic flux).
- The rate at which the coil is rotated (affecting the angle \(\theta\) and thus the flux).

4. **Identifying What Induced EMF Does Not Depend On**:
One important factor that does not affect the induced e.m.f. is the **resistance of the circuit**. While resistance affects the current flowing through the circuit, it does not influence the amount of induced e.m.f. itself.

5. **Conclusion**:
Therefore, the induced e.m.f. in a coil does not depend on the resistance of the circuit.

### Final Answer:
The induced e.m.f. in a coil does not depend on the resistance of the circuit.