A transformer has 200 turns on primary side and 20 turns on secondary side. If we apply 200 V DC on its primary side, then voltage at the secondary is:

Explanation:

Transformers and DC Voltage

Definition: A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It typically consists of two windings, the primary and the secondary, wound around a magnetic core. The primary winding is connected to the input voltage source, and the secondary winding delivers the transformed voltage to the load.

Working Principle: Transformers operate on the principle of electromagnetic induction, specifically Faraday's Law of Induction. When an alternating current (AC) flows through the primary winding, it creates a time-varying magnetic field in the core. This changing magnetic field induces an electromotive force (EMF) in the secondary winding. The voltage induced in the secondary winding is proportional to the number of turns in the primary and secondary windings, following the transformer equation:

Transformer Equation:

V_s/V_p = N_s/N_p

Where:

• V_s = Voltage in the secondary winding
• V_p = Voltage in the primary winding
• N_s = Number of turns in the secondary winding
• N_p = Number of turns in the primary winding

Transformers are designed to operate with AC voltage because the changing current is necessary to create a changing magnetic field. This changing magnetic field is what induces the voltage in the secondary winding.

DC Voltage and Transformers:

When a direct current (DC) voltage is applied to the primary winding of a transformer, the current does not change with time (assuming a constant DC voltage). As a result, there is no time-varying magnetic field generated in the core. Without a changing magnetic field, no EMF is induced in the secondary winding. Consequently, the secondary voltage will be zero.

Detailed Solution:

Given the parameters:

• Primary turns (N_p) = 200
• Secondary turns (N_s) = 20
• Primary voltage (V_p) = 200 V (DC)

When 200 V DC is applied to the primary winding:

• Since the applied voltage is DC, the current in the primary winding is constant.
• A constant current produces a constant magnetic field in the core.
• A constant magnetic field does not induce any EMF in the secondary winding.

Therefore, the voltage in the secondary winding (V_s) is 0 V.

Correct Option Analysis:

The correct option is:

Option 3: 0 V

This option correctly reflects that no voltage will be induced in the secondary winding of the transformer when a DC voltage is applied to the primary winding.

Additional Information

To further understand the analysis, let’s evaluate the other options:

Option 1: 200 V

This option is incorrect because it assumes that the transformer will step up or step down the DC voltage. However, a transformer cannot induce any voltage in the secondary winding with a DC input, as explained above.

Option 2: 20 V

This option is incorrect for the same reason. It assumes the transformer will step down the DC voltage. Since there is no changing magnetic field with a DC input, no voltage is induced in the secondary winding.

Option 4: 100 V

This option is also incorrect. It implies a step-down transformation that is not possible with a DC input, as no voltage will be induced in the secondary winding.

Conclusion:

Understanding the operation of transformers with different types of input voltage is crucial. Transformers are designed to work with AC voltage, which creates a changing magnetic field necessary for inducing voltage in the secondary winding. When a DC voltage is applied, no changing magnetic field is produced, and thus, no voltage is induced in the secondary winding. This analysis highlights the fundamental principle that transformers cannot operate with DC voltage inputs, leading to a secondary voltage of 0 V in such cases.