A explain the operating principle of a transformers

b a 10 kva singlephase transformers has a turn ratio of 121 and is supplied from a 24 kv supply neglecting losses
determine
i the full load secondary current

ii the minimum value of load

Question

a) Explain the operating principle of a transformers.

b) A 10 kVA, single-phase transformers has a turn ratio of 12:1 and is supplied from a 2.4 kV supply. Neglecting losses, determine:
i. the full load secondary current.

ii. the minimum value of load resistance which can be connected across the secondary winding.

iii. the primary current.

Audrey Perry · Answer

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.

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.
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.
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:

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

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

$S = V_2 imes I_2$

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

ii. Minimum Value of Load Resistance:

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

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

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

iii. Primary Current:

To find the primary current ( $I_1$ ):

First, use the turns ratio relationship for current:

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

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

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

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