In an ideal transformer the number turns of primary and secondary coil is given as 100 and 200 respectively. If the peak value of the primary voltage is 50V, then the r.m.s value of secondary voltage is nearest to

Options

A. 100V
B. 200V
C. 60V
D. 70V

Answer

To solve the problem step by step, we will use the relationship between the primary and secondary coils of an ideal transformer.

### Step 1: Understand the transformer relationship
In an ideal transformer, the relationship between the primary and secondary voltages and the number of turns in the coils is given by the formula:

\[ \frac{V_p}{V_s} = \frac{N_p}{N_s} \]

Where:
- \( V_p \) = Primary voltage
- \( V_s \) = Secondary voltage
- \( N_p \) = Number of turns in the primary coil
- \( N_s \) = Number of turns in the secondary coil

### Step 2: Identify the given values
From the problem, we have:
- \( N_p = 100 \) (number of turns in the primary coil)
- \( N_s = 200 \) (number of turns in the secondary coil)
- \( V_p = 50 \, V \) (peak value of the primary voltage)

### Step 3: Calculate the secondary voltage
Using the transformer relationship, we can rearrange the formula to find \( V_s \):

\[ V_s = V_p \times \frac{N_s}{N_p} \]

Substituting the known values:

\[ V_s = 50 \, V \times \frac{200}{100} \]

\[ V_s = 50 \, V \times 2 = 100 \, V \]

### Step 4: Convert the peak voltage to RMS voltage
The RMS (Root Mean Square) value of an AC voltage is related to its peak value by the formula:

\[ V_{rms} = \frac{V_{peak}}{\sqrt{2}} \]

Since we found the secondary voltage \( V_s \) to be 100 V (which is the peak voltage), we can calculate the RMS value:

\[ V_{s, rms} = \frac{100 \, V}{\sqrt{2}} \approx \frac{100}{1.414} \approx 70.71 \, V \]

### Step 5: Round to the nearest value
The nearest value to 70.71 V is approximately 70 V.

### Final Answer
The RMS value of the secondary voltage is nearest to **70 V**.

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