Which of the following can produce maximum induced emf?

Options

A. 50 ampere DC
B. 50 ampere 50 Hz AC
C. 50 ampere 500 Hz AC
D. 100 ampere DC

Answer

To determine which option can produce the maximum induced electromotive force (emf), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Induced EMF**:
The induced emf (E) in a coil is given by Faraday's law of electromagnetic induction, which states:
\[ E = -\frac{d\Phi}{dt} \]
where \( \Phi \) is the magnetic flux linked with the coil. The negative sign indicates the direction of the induced emf (Lenz's law).

2. **Analyzing the Options**:
- **Option 1: 15 ampere DC**:
In direct current (DC), the current is constant and does not change with time. Therefore, there is no change in magnetic flux, leading to:
\[ \frac{d\Phi}{dt} = 0 \quad \Rightarrow \quad E = 0 \]
This option cannot produce induced emf.

- **Option 2: 15 ampere 50 Hertz AC**:
Alternating current (AC) changes direction and magnitude periodically. At 50 Hertz, the current changes 50 times per second, which means there is a change in magnetic flux. However, the rate of change of flux is lower compared to higher frequencies.

- **Option 3: 15 ampere 500 Hertz AC**:
At 500 Hertz, the current changes direction and magnitude 500 times per second. This results in a greater rate of change of magnetic flux compared to 50 Hertz, leading to a larger induced emf.

- **Option 4: 15 ampere DC**:
This is the same as Option 1 and will also produce no induced emf for the same reasons.

3. **Conclusion**:
Comparing the AC options, the higher the frequency, the greater the rate of change of magnetic flux and thus the greater the induced emf. Therefore, the option that produces the maximum induced emf is:
\[ \text{Option 3: 15 ampere 500 Hertz AC} \]