A 50 Hz AC current of crest value 1 A flows through the primary of a transformer. If the mutual inductance between the promary and secondary be 0.5 H, the creast voltage induced in the secondary is

Options

A. 75 V
B. 150 V
C. 100 V
D. None of these

Answer

To solve the problem, we need to find the crest voltage induced in the secondary of a transformer given the frequency of the AC current, the crest value of the current, and the mutual inductance.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Frequency (f) = 50 Hz
- Crest value of current (I_max) = 1 A
- Mutual inductance (M) = 0.5 H

2. **Calculate the Time Period (T):**
The time period (T) can be calculated using the formula:
\[ T = \frac{1}{f} \]
Substituting the given frequency:
\[ T = \frac{1}{50} = 0.02 \text{ seconds} \]

3. **Determine the Change in Current (ΔI):**
The change in current (ΔI) from the crest value is:
\[ ΔI = I_{max} - (-I_{max}) = 1 - (-1) = 2 \text{ A} \]

4. **Calculate the Change in Time (Δt):**
The change in time (Δt) for half a cycle is:
\[ Δt = \frac{T}{2} = \frac{0.02}{2} = 0.01 \text{ seconds} \]

5. **Calculate the Rate of Change of Current (dI/dt):**
The rate of change of current can be calculated as:
\[ \frac{dI}{dt} = \frac{ΔI}{Δt} = \frac{2}{0.01} = 200 \text{ A/s} \]

6. **Calculate the Induced Voltage (V):**
The induced voltage in the secondary can be calculated using the formula:
\[ V = M \frac{dI}{dt} \]
Substituting the values:
\[ V = 0.5 \times 200 = 100 \text{ V} \]

### Final Answer:
The crest voltage induced in the secondary is **100 V**.