Transformer Secondary EMF Calculation

A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction. It is commonly used to increase or decrease AC voltages. The relationship between the voltages and the number of turns in the primary and secondary windings of an ideal transformer is crucial for understanding its operation.

Transformer Principles

The core principle governing a transformer's operation is the transformer turns ratio. This ratio relates the primary voltage to the secondary voltage based on the number of turns in each winding. Additionally, a key characteristic of transformers is that they do not change the frequency of the AC supply.

Given Transformer Parameters

Let's list the given parameters for this transformer question:

• Primary turns (\(N_p\)): 350 turns
• Secondary turns (\(N_s\)): 1050 turns
• Primary voltage (\(V_p\)): 230 V
• Primary frequency (\(f_p\)): 50 Hz

Secondary Voltage Calculation

To find the induced EMF (voltage) in the secondary winding, we use the transformer turns ratio formula:

\[\frac{V_s}{V_p} = \frac{N_s}{N_p}\]

Where:

• \(V_s\) is the secondary voltage (induced EMF)
• \(V_p\) is the primary voltage
• \(N_s\) is the number of turns in the secondary winding
• \(N_p\) is the number of turns in the primary winding

Rearranging the formula to solve for \(V_s\):

\[V_s = V_p \times \frac{N_s}{N_p}\]

Now, let's substitute the given values into the formula:

\[V_s = 230 \, \text{V} \times \frac{1050 \, \text{turns}}{350 \, \text{turns}}\]

First, simplify the turns ratio:

\[\frac{1050}{350} = 3\]

Now, multiply this ratio by the primary voltage:

\[V_s = 230 \, \text{V} \times 3\]

\[V_s = 690 \, \text{V}\]

So, the induced EMF in the secondary winding is 690 V.

Secondary Frequency Determination

A fundamental characteristic of an ideal transformer is that it does not alter the frequency of the AC voltage and current. The frequency of the induced EMF in the secondary winding will always be the same as the frequency of the AC supply connected to the primary winding.

Given the primary frequency (\(f_p\)) is 50 Hz, the secondary frequency (\(f_s\)) will also be:

\[f_s = f_p = 50 \, \text{Hz}\]

Final Result

Combining both the calculated secondary voltage and frequency, the induced EMF in the secondary will be 690 V, 50 Hz.