Questions

a) Operating Principle of a Transformer:

A transformer operates on the principle of electromagnetic induction and mutual induction between two or more windings (or coils). The core of the transformer is typically made from laminated steel to minimize eddy current losses.

1. Primary Winding: The primary winding receives an alternating current (AC) voltage source. When an AC voltage is applied, it creates a time-varying magnetic field around the winding.

2. Magnetic Core: The magnetic field generated by the primary winding induces a magnetic flux in the core of the transformer. This flux travels through the core to the secondary winding.

3. Secondary Winding: The changing magnetic flux in the core induces an alternating voltage across the secondary winding through electromagnetic induction.

• Turns Ratio: The ratio of the number of turns in the primary winding ($N_1$) to the number of turns in the secondary winding ($N_2$) is called the turns ratio and it determines the relationship between the input (primary) voltage and output (secondary) voltage.

$\frac{V_1}{V_2} = \frac{N_1}{N_2}$

Where:

• $V_1$ = Primary voltage

• $V_2$ = Secondary voltage

• Impedance Transformation: The turns ratio also affects the ratio of the primary and secondary currents.

$\frac{I_2}{I_1} = \frac{N_1}{N_2}$

Where:

• $I_1$ = Primary current
• $I_2$ = Secondary current

Transformers are used to increase (step-up) or decrease (step-down) voltage levels while ideally maintaining the same power (neglecting losses).

b) Transformer Calculations:

Given:

• Power rating $S$ = 10 kVA (10,000 VA)
• Turns ratio ($N_1:N_2$) = 12:1
• Primary voltage ($V_1$) = 2.4 kV (2,400 V)

i. Full Load Secondary Current:

To determine the full load secondary current ($I_2$):

Step 1: Determine the secondary voltage ($V_2$):

Given $\frac{V_1}{V_2} = 12$, so:

$V_2 = \frac{V_1}{12} = \frac{2400 \text{ V}}{12} = 200 \text{ V}$

Step 2: Use the power equation to find $I_2$:

$S = V_2 \times I_2$

$I_2 = \frac{S}{V_2} = \frac{10,000 \text{ VA}}{200 \text{ V}} = 50 \text{ A}$

ii. Minimum Value of Load Resistance:

To determine the minimum load resistance ($R_L$) that can be connected across the secondary winding:

$R_L = \frac{V_2}{I_2}$

$R_L = \frac{200 \text{ V}}{50 \text{ A}} = 4 \text{ ohms}$

iii. Primary Current:

To find the primary current ($I_1$):

First, use the turns ratio relationship for current:

$\frac{I_2}{I_1} = 12$

$I_1 = \frac{I_2}{12} = \frac{50 \text{ A}}{12} \approx 4.17 \text{ A}$

Therefore, the full load primary current is approximately 4.17 A.