Question

In an ideal transformer, the turns ratio is \(N_p/N_s\) =1/2 .The ratio \(V_S:V_P\)  is equal to (the symbols carry their usual meaning):

• A. 1:2
• B. 2:1
• C. 1:1
• D. 1:4

Answer 1

The Correct Option is B

In an ideal transformer, the turns ratio is given by the equation: \(\frac{N_p}{N_s} = \frac{V_p}{V_s}\), where:

• \(N_p\) is the number of turns in the primary coil.
• \(N_s\) is the number of turns in the secondary coil.
• \(V_p\) is the voltage across the primary coil.
• \(V_s\) is the voltage across the secondary coil.

In this scenario, the turns ratio is \( \frac{N_p}{N_s} = \frac{1}{2} \). Plugging this into the transformer equation, we have:

\(\frac{V_p}{V_s} = \frac{1}{2}\)

This implies that:

\(V_s = 2 \times V_p\)

Thus, the voltage ratio \( V_S:V_P \) is: \(2:1\)

The correct answer is 2:1

Answer 2

Step 1: Understand the Relationship in an Ideal Transformer 

In an ideal transformer, the relationship between the primary and secondary voltage is given by:

$$ \frac{V_P}{V_S} = \frac{N_P}{N_S} $$

• V_P = Primary voltage
• V_S = Secondary voltage
• N_P = Number of primary turns
• N_S = Number of secondary turns

Step 2: Substitute the Turns Ratio into the Equation

The turns ratio is given as:

$$ \frac{N_P}{N_S} = \frac{1}{2} $$

Thus, the voltage ratio becomes:

$$ \frac{V_P}{V_S} = \frac{N_P}{N_S} $$

Step 3: Determine \( V_S : V_P \)

Rewriting the ratio of \( V_P \) to \( V_S \):

$$ \frac{N_P}{N_S} = \frac{1}{2} $$

$$ \frac{V_P}{V_S} = \frac{1}{2} \Rightarrow \frac{V_S}{V_P} = 2:1 $$

Conclusion:

The ratio V_S : V_P is 2 : 1, which matches option (2).