91Ó°ÊÓ

In the world of transformers, the turns ratio is a fundamental concept that defines the relationship between the coils. The turns ratio compares the number of turns in the primary coil to the number of turns in the secondary coil. For instance, a turns ratio of 1:8 indicates that for every single turn in the primary coil, there are eight turns in the secondary coil.
This ratio is critical because it directly influences how voltage and current are transformed from one coil to the other. Essentially, it helps in predicting how much the voltage is either increased or decreased. The turns ratio can also be expressed as a fraction, where you place the number of secondary turns over the number of primary turns, in this case, 8/1. It's also noteworthy that:

• If the secondary coil has more turns than the primary coil, it results in a step-down transformer.
• The opposite is true for a step-up transformer.

A step-down transformer serves the important function of reducing voltage levels. They are commonly used in systems where devices require a different—usually lower—voltage than is provided by the source. Such is the case with the electric train in our exercise, needing a reduced voltage from the wall outlet.
A step-down transformer works on the principle of electromagnetic induction and uses the turns ratio to provide the desired output. In a step-down transformer:

• The secondary coil has more turns than the primary coil.
• This arrangement decreases the voltage while correspondingly increasing the current.

An important relationship to remember is that while the voltage decreases, the power (the product of voltage and current) ideally remains the same due to energy conservation. Therefore, any decrease in voltage results in an increase in current, providing the necessary energy for devices like an electric train.

The primary coil current (I_p) is the current flowing through the primary coil of the transformer. It's determined by the current in the secondary coil and the turns ratio of the transformer. To find the primary coil current, we use the transformer current equation:\[\frac{I_p}{I_s} = \frac{N_s}{N_p}\]Where:

• I_s is the secondary current (1.6 A in this case).
• N_s and N_p are the number of turns in the secondary and primary coils, respectively.

Our original problem had a turns ratio of 1:8 and a secondary current of 1.6 A. Plugging in these values, we rearrange the equation to solve for I_p:\[I_p = I_s \times \frac{N_p}{N_s}\]Substitute the known values, we get:\[I_p = 1.6 \times \frac{1}{8} = 0.2 \, \text{A}\]Thus, the primary coil conducts a current of 0.2 A, showcasing how the transformer balances its functions between its coils.

The secondary coil current is the current flowing through the secondary coil, which in this exercise is known to be 1.6 A. This current value is pivotal because it sets the stage for calculating the primary current using the turns ratio.
The secondary coil current is often higher than the primary coil current in a step-down transformer. This happens because while the voltage drops, the current rises to keep the power constant, in an ideal scenario.
It is important to note that the relationship between primary and secondary currents ensures that power equations hold true. By utilizing the transformer formulas:

• We see that the turns ratio directly informs us of how the currents will scale.
• Understanding this scaling effect helps in engineering solutions where precise voltage and current levels are required.