A current transformer has single turn primary and 200 turns secondary winding. It is used for measurement of AC current by connecting an ammeter of 5 Amp. (Full scale deflection). What is the maximum value of the primary current that can be measured with this arrangement?

Explanation:

Current Transformer Analysis

Definition: A current transformer (CT) is an instrument transformer designed to produce an alternating current (AC) in its secondary winding, which is proportional to the AC current in its primary winding. CTs are commonly used for measuring high currents by stepping down the current to a lower, safer level that can be easily measured by standard ammeters and other instruments.

Given Data:

• Primary winding: 1 turn
• Secondary winding: 200 turns
• Ammeter full-scale deflection: 5 A

Working Principle: The primary and secondary windings of the current transformer are connected in such a way that the magnetic flux produced by the current in the primary winding induces a current in the secondary winding. The ratio of the primary current (Ip) to the secondary current (Is) is inversely proportional to the turns ratio of the windings.

Turns Ratio: The turns ratio (Np:Ns) of the current transformer is given by the ratio of the number of turns in the primary winding (Np) to the number of turns in the secondary winding (Ns).

In this case, we have:

Np = 1 turn

Ns = 200 turns

The turns ratio (Np:Ns) = 1:200

Current Ratio: The current ratio of the current transformer is given by the ratio of the primary current (Ip) to the secondary current (Is). Since the ammeter is connected to the secondary winding and is designed to measure up to 5 A for full-scale deflection, we can calculate the maximum primary current (Ip_max) that can be measured using the turns ratio.

Let Ip_max be the maximum primary current and Is_max be the maximum secondary current (which is 5 A in this case).

The current ratio can be expressed as:

Ip/Is = Ns/Np

Substituting the given values:

Ip_max / 5 A = 200 / 1

Solving for Ip_max:

Ip_max = 5 A * (200 / 1)

Ip_max = 1000 A

Therefore, the maximum value of the primary current that can be measured with this arrangement is 1000 A.

Advantages:

• Current transformers allow the measurement of high currents safely and accurately by stepping down the current to a lower level suitable for standard instruments.
• They provide electrical isolation between the high-current primary circuit and the measuring instruments.

Disadvantages:

• Current transformers can introduce errors due to their inherent inaccuracies and phase shifts.
• Saturation of the core can occur at high currents, leading to measurement inaccuracies.

Applications: Current transformers are widely used in power systems for metering and protection purposes. They are employed in substations, switchgear, and industrial applications to measure and monitor high currents.

Correct Option Analysis:

The correct option is:

Option 1: 1000 A

This option correctly identifies the maximum value of the primary current that can be measured using the given current transformer with a turns ratio of 1:200 and an ammeter with a full-scale deflection of 5 A.

Additional Information

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

Option 2: 5000 A

This option is incorrect because it overestimates the maximum primary current. Given the turns ratio of 1:200 and the ammeter's full-scale deflection of 5 A, the correct calculation yields a maximum primary current of 1000 A, not 5000 A.

Option 3: 40 A

This option is incorrect because it underestimates the maximum primary current. The correct calculation based on the given data yields a maximum primary current of 1000 A.

Option 4: 200 A

This option is also incorrect as it does not align with the correct calculation. The maximum primary current, based on the turns ratio and the ammeter's specifications, is 1000 A, not 200 A.

Conclusion:

Understanding the principles of current transformers and their turns ratio is crucial for accurately determining the maximum primary current that can be measured. The correct option, as explained, is 1000 A, which is derived from the given turns ratio of 1:200 and the ammeter's full-scale deflection of 5 A. Current transformers play a vital role in safely measuring high currents and ensuring electrical isolation in various applications.