A `220 V` input is supplied to a transformer. The output circuit draws a current of `2.0 A` at `440 V`. If the efficiency of the transformer is `80%`, the current drawn by the primery winding of the transformer is:
(1.) 3.6A
(2.) 2.8A
(3.) 2.5A
(4.) 5.0A

Options

A. `3.6A`
B. `2.8A`
C. `2.5A`
D. `5.0A`

Answer

To find the current drawn by the primary winding of the transformer, we can use the formula for the efficiency of the transformer. The efficiency (η) is given by the formula:

\[ \eta = \frac{V_s \cdot I_s}{V_p \cdot I_p} \]

Where:
- \( V_s \) = Secondary voltage
- \( I_s \) = Secondary current
- \( V_p \) = Primary voltage
- \( I_p \) = Primary current

Given:
- \( V_s = 440 \, V \)
- \( I_s = 2.0 \, A \)
- \( V_p = 220 \, V \)
- \( \eta = 80\% = 0.8 \)

We need to find \( I_p \).

### Step 1: Rearranging the efficiency formula
We can rearrange the efficiency formula to solve for \( I_p \):

\[ I_p = \frac{V_s \cdot I_s}{\eta \cdot V_p} \]

### Step 2: Substituting the known values
Now, we can substitute the known values into the rearranged formula:

\[ I_p = \frac{440 \, V \cdot 2.0 \, A}{0.8 \cdot 220 \, V} \]

### Step 3: Calculating the numerator
Calculating the numerator:

\[ 440 \, V \cdot 2.0 \, A = 880 \, VA \]

### Step 4: Calculating the denominator
Calculating the denominator:

\[ 0.8 \cdot 220 \, V = 176 \, V \]

### Step 5: Dividing the numerator by the denominator
Now, we divide the numerator by the denominator to find \( I_p \):

\[ I_p = \frac{880 \, VA}{176 \, V} = 5.0 \, A \]

### Final Answer
Thus, the current drawn by the primary winding of the transformer is:

\[ \boxed{5.0 \, A} \]