Understanding Current Transformers (CT) and Ammeters

A current transformer (CT) is a device used in electrical power systems to measure high alternating currents safely. It works on the principle of electromagnetic induction to produce a reduced current in its secondary winding that is proportional to the current flowing in its primary winding. This reduced current can then be easily measured by standard instruments like an ammeter, which typically has a rating of 5 A.

In this problem, we are given:

• The ratio of the current transformer (CT) is 100 : 5. This means for every 100 units of current flowing through the primary winding (which is the line conductor), 5 units of current will flow through the secondary winding.
• The ammeter, connected to the secondary winding of the CT, reads 3.5 A. This reading represents the secondary current.

Calculating the Line Current

The relationship between the primary current (line current), secondary current (ammeter reading), and the CT ratio can be expressed as:

$$ \text{CT Ratio} = \frac{\text{Primary Current}}{\text{Secondary Current}} $$

We can rearrange this formula to find the Primary Current (Line Current):

$$ \text{Primary Current} = \text{CT Ratio} \times \text{Secondary Current} $$

The CT ratio is given as 100:5, which can be written as a factor:

$$ \text{CT Factor} = \frac{100}{5} = 20 $$

The secondary current, as read by the ammeter, is 3.5 A.

Step-by-Step Calculation:

1. Identify the CT ratio: 100:5.
2. Calculate the CT ratio factor: $ \frac{100}{5} = 20 $.
3. Identify the ammeter reading (Secondary Current): 3.5 A.
4. Calculate the Line Current (Primary Current):

   $$ \text{Line Current} = \text{CT Factor} \times \text{Secondary Current} $$

   $$ \text{Line Current} = 20 \times 3.5 \, \text{A} $$

   $$ \text{Line Current} = 70 \, \text{A} $$

Therefore, the actual line current is 70 A.