A transformer of 100 % efficiency has 200 turns in the primary and 40,000 turns in the secondary. It is connected to a 220 V a.c. mains and the secondary feeds to a `100 k Omega` resistance. Calculate the output potential difference per turn and the power delivered to the load.

Options

A. 1.1 V
B. 25 V
C. 18 V
D. 11 V

Explanation

To solve the problem step by step, we will use the transformer equations and the given values.

### Step 1: Understand the Transformer Ratio
The transformer ratio relates the primary voltage (Vp), secondary voltage (Vs), primary turns (Np), and secondary turns (Ns) as follows:
\[ \frac{V_s}{V_p} = \frac{N_s}{N_p} \]

### Step 2: Substitute the Known Values
We know:
- \( V_p = 220 \, \text{V} \)
- \( N_p = 200 \)
- \( N_s = 40000 \)

Using the transformer ratio formula, we can express \( V_s \):
\[ V_s = V_p \times \frac{N_s}{N_p} \]

### Step 3: Calculate the Secondary Voltage (Vs)
Substituting the known values into the equation:
\[ V_s = 220 \times \frac{40000}{200} \]
Calculating the fraction:
\[ \frac{40000}{200} = 200 \]
Now substituting this back:
\[ V_s = 220 \times 200 = 44000 \, \text{V} \]

### Step 4: Calculate the Output Potential Difference per Turn
The potential difference per turn in the secondary coil can be calculated using:
\[ \text{Potential difference per turn} = \frac{V_s}{N_s} \]
Substituting the values:
\[ \text{Potential difference per turn} = \frac{44000}{40000} \]
Calculating this gives:
\[ \text{Potential difference per turn} = 1.1 \, \text{V} \]

### Step 5: Calculate the Power Delivered to the Load
The power delivered to the load (P) can be calculated using:
\[ P = \frac{V_s^2}{R} \]
Where \( R = 100 \, k\Omega = 100000 \, \Omega \).

Substituting the values:
\[ P = \frac{(44000)^2}{100000} \]
Calculating \( (44000)^2 \):
\[ (44000)^2 = 1936000000 \]
Now substituting this value:
\[ P = \frac{1936000000}{100000} = 19360 \, \text{W} \]

### Final Results
- The output potential difference per turn is \( 1.1 \, \text{V} \).
- The power delivered to the load is \( 19360 \, \text{W} \).