Question

A 200/100 V transformer has a primary resistance of 0.1 $\Omega$. What is this resistance when referred to the secondary side?

• A. 0.4 $\Omega$
• B. 0.2 $\Omega$
• C. 0.05 $\Omega$
• D. 0.025 $\Omega$

Hint:

Referral Rules:
- High-Voltage (HV) to Low-Voltage (LV) side: Resistance decreases by \(k^2\) (or \(a^2\)).
- Low-Voltage (LV) to High-Voltage (HV) side: Resistance increases.
Since the primary (200 V) is the high-voltage side and the secondary (100 V) is the low-voltage side, the referred resistance must be smaller than the original \(0.1\ \Omega\). This eliminates options (A) and (B) instantly.

Answer 1

The Correct Option is D

Step 1: Understanding the Problem:
The question asks to refer (or scale) the electrical resistance of the primary winding of a transformer to its secondary winding side, given the transformer's voltage ratings.

Step 2: Key Formula or Approach:
Let the turns ratio (or transformation ratio) of the transformer be \(k\), defined as:
\[ k = \frac{V_2}{V_1} = \frac{N_2}{N_1} \] When transferring a resistance from the primary side (\(R_1\)) to the secondary side (\(R_1'\)), the value is scaled by the square of the transformation ratio:
\[ R_1' = R_1 \times k^2 = R_1 \times \left(\frac{V_2}{V_1}\right)^2 \]

Step 3: Detailed Explanation:

• Identify the given parameters from the problem:
- Primary voltage, \(V_1 = 200\text{ V}\).
- Secondary voltage, \(V_2 = 100\text{ V}\).
- Primary winding resistance, \(R_1 = 0.1\ \Omega\).

• Calculate the transformation ratio \(k\):
\[ k = \frac{V_2}{V_1} = \frac{100}{200} = 0.5 \]
• Apply the referral formula to find the resistance referred to the secondary side:
\[ R_1' = R_1 \times k^2 \] \[ R_1' = 0.1 \times (0.5)^2 \] \[ R_1' = 0.1 \times 0.25 = 0.025\ \Omega \]

Step 4: Final Answer:
The primary resistance referred to the secondary side is \(0.025\ \Omega\).