Question

Primary coil of a transformer is connected to 220 V ac. Primary and secondary turns of the transforms are 100 and 10 respectively. Secondary coil of transformer is connected to two series resistance shown in shown in figure. The output voltage (V0) is :

• A. 15 V
• B. 7 V
• C. 44 V
• D. 22 V

Answer 1

The Correct Option is B

The objective is to compute the output voltage (\(V_0\)) of a circuit comprising a transformer followed by a resistive voltage divider.

Core Principles:

The solution employs two fundamental principles:

1. Transformer Relationship: For an ideal transformer, the voltage ratio across its coils is directly proportional to the turns ratio: \( \frac{V_s}{V_p} = \frac{N_s}{N_p} \).

2. Voltage Divider Formula: For resistors in series, the voltage across a specific resistor is given by: \( V_{out} = V_{in} \times \frac{R_{out}}{R_{total}} \).

Solution Breakdown:

Step 1: Determine the secondary voltage (\(V_s\)) of the transformer.

Given transformer parameters:

• Primary voltage: \(V_p = 220 \, \text{V}\)
• Primary turns: \(N_p = 100\)
• Secondary turns: \(N_s = 10\)

Applying the transformer equation:

\[\frac{V_s}{220 \, \text{V}} = \frac{10}{100}\]

Calculation yields:

\[V_s = 220 \times \frac{1}{10} = 22 \, \text{V}\]

This secondary voltage serves as the input to the subsequent resistive network.

Step 2: Model the secondary circuit as a voltage divider.

The secondary circuit consists of two series resistors:

• \(R_1 = 15 \, \text{k}\Omega\)
• \(R_2 = 7 \, \text{k}\Omega\)

The total series resistance is:

\[R_{total} = R_1 + R_2 = 15 \, \text{k}\Omega + 7 \, \text{k}\Omega = 22 \, \text{k}\Omega\]

The output voltage \(V_0\) is the voltage across \(R_2\), thus \(R_{out} = 7 \, \text{k}\Omega\).

Step 3: Compute the output voltage \(V_0\) using the voltage divider rule.

The input voltage to the divider is \(V_{in} = V_s = 22 \, \text{V}\).

\[V_0 = V_{in} \times \frac{R_{out}}{R_{total}}\]\[V_0 = 22 \, \text{V} \times \frac{7 \, \text{k}\Omega}{22 \, \text{k}\Omega}\]

Final Calculation and Outcome:

Simplifying the expression for \(V_0\):

\[V_0 = 22 \times \frac{7}{22}\]\[V_0 = 7 \, \text{V}\]

The calculated output voltage \(V_0\) is 7 V.