If the input voltage of a transformer is 2500 volts and output current is 80 ampere . The ratio of number of turns in the primary coil to that in secondary coil is 20 : 1 . If efficiency of transformer is 100 % , then the voltage in secondary coil as :

Options

A. `(2500)/20` volt
B. `2500xx20`volt
C. `2500/(80 xx20)` volt
D. `(2500 xx20)/80`volt

Answer

To find the voltage in the secondary coil of the transformer, we can use the relationship between the primary and secondary voltages and the turns ratio of the transformer. Here's the step-by-step solution:

### Step 1: Understand the transformer relationships
In a transformer, the relationship between the primary voltage (Vp), secondary voltage (Vs), primary current (Ip), secondary current (Is), and the turns ratio (Np/Ns) is given by the following equations:
1. \( \frac{V_p}{V_s} = \frac{N_p}{N_s} \)
2. \( P_{in} = P_{out} \) (for 100% efficiency)

Where:
- \( V_p \) = Primary voltage
- \( V_s \) = Secondary voltage
- \( N_p \) = Number of turns in the primary coil
- \( N_s \) = Number of turns in the secondary coil

### Step 2: Identify the given values
From the question, we have:
- Input voltage \( V_p = 2500 \, \text{volts} \)
- Output current \( I_s = 80 \, \text{amperes} \)
- Turns ratio \( \frac{N_p}{N_s} = 20:1 \)

### Step 3: Calculate the output voltage using the turns ratio
Using the turns ratio, we can rearrange the first equation to find the secondary voltage:
\[ V_s = \frac{V_p \cdot N_s}{N_p} \]

Given the turns ratio \( \frac{N_p}{N_s} = 20:1 \), we can express \( N_s \) in terms of \( N_p \):
\[ N_s = \frac{N_p}{20} \]

Substituting \( N_s \) into the equation for \( V_s \):
\[ V_s = \frac{V_p \cdot \frac{N_p}{20}}{N_p} = \frac{V_p}{20} \]

### Step 4: Substitute the known values
Now, substituting the known value of \( V_p \):
\[ V_s = \frac{2500 \, \text{volts}}{20} \]

### Step 5: Perform the calculation
Calculating \( V_s \):
\[ V_s = 125 \, \text{volts} \]

### Final Answer
The voltage in the secondary coil is **125 volts**.

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