Question

A step up transformer operates on $220\text{ V}$ and supplies current of $2\text{ A}$. The ratio of primary and secondary windings is $1 : 20$. The current in the primary is

• A. $5\text{ A}$
• B. $2\text{ A}$
• C. $40\text{ A}$
• D. $20\text{ A}$

Hint:

A step-up transformer increases voltage but must proportionally step down the current to satisfy conservation of energy. Since the secondary side has 20 times more loops, its voltage scales up by 20, which forces its current to drop by a factor of 20. Therefore, the primary current must simply be $2\text{ A} \times 20 = 40\text{ A}$.

Answer 1

The Correct Option is C

Step 1: Use current-turns inversion.
In an ideal transformer the current ratio is the inverse of the turns ratio, so we do not even need the voltage value.
Step 2: State the relation.
$\dfrac{I_p}{I_s} = \dfrac{N_s}{N_p}$, i.e. the side with more turns carries less current.
Step 3: Read the turns ratio.
$\dfrac{N_p}{N_s} = \dfrac{1}{20}$, so $\dfrac{N_s}{N_p} = 20$.
Step 4: Apply it to currents.
$I_p = I_s \times \dfrac{N_s}{N_p} = 2 \times 20$.
Step 5: Evaluate.
$I_p = 40\,\text{A}$.
Step 6: Sanity check.
A step-up transformer raises voltage but lowers secondary current, so the primary side carries the larger current, consistent with $40\,\text{A} > 2\,\text{A}$. \[ \boxed{I_p = 40\ \text{A}} \]