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 solve the problem step by step, we will use the properties of an ideal transformer and the given data.

### Step 1: Understand the transformer relationships
For an ideal transformer, the following relationships hold:
1. \( \frac{N_s}{N_p} = \frac{V_s}{V_p} = \frac{I_p}{I_s} \)
Where:
- \( N_s \) = number of turns in the secondary coil
- \( N_p \) = number of turns in the primary coil
- \( V_s \) = voltage in the secondary coil
- \( V_p \) = voltage in the primary coil
- \( I_s \) = current in the secondary coil
- \( I_p \) = current in the primary coil

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

### Step 3: Use the transformer relationship to find \( V_s \)
Using the relationship \( \frac{N_s}{N_p} = \frac{V_s}{V_p} \), we can express \( V_s \):
\[ \frac{N_s}{N_p} = \frac{1}{20} \implies \frac{V_s}{2500} = \frac{1}{20} \]

### Step 4: Cross-multiply to solve for \( V_s \)
Cross-multiplying gives:
\[ V_s = 2500 \times \frac{1}{20} \]

### Step 5: Calculate \( V_s \)
Now we calculate \( V_s \):
\[ V_s = \frac{2500}{20} = 125 \text{ volts} \]

### Final Answer
The voltage in the secondary coil is \( 125 \) volts.

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