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Test: Equivalent Circuit of Transformer - Electrical Engineering (EE) MCQ


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10 Questions MCQ Test Electrical Machines for Electrical Engg. - Test: Equivalent Circuit of Transformer

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Test: Equivalent Circuit of Transformer - Question 1

If a 2200/220 V, 60 Hz single phase transformer has primary and secondary resistance of 100 Ω and 10 Ω, respectively. Then the value of equivalent resistance of the transformer referred to the primary side and secondary side are

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 1

Concept:

In a transformer, the turns ratio is given by

Where V1 is the primary voltage

V2 is the secondary voltage

N1 is the primary turns

N2 is the secondary turns

I1 is the primary current

Iis the secondary current

The equivalent resistance of the transformer referred to the primary side = R1 + n2R2

The equivalent resistance of the transformer referred to the secondary side = R2 + R1/n2

Calculation:

Given that, primary voltage (V1) = 2200 V

Secondary voltage (V2) = 220 V

Primary resistance (R1) =100 Ω

Secondary resistance (R2) = 10 Ω

Turns ratio = 2200/220 = 10

∴ Equivalent resistance of the transformer referred to the primary side

=> R1 + n2R2 = [100 + (10)2 × 10] = 1100 Ω

∴ Equivalent resistance of the transformer referred to the secondary side

=> R2 + R1/n2 = [10 + 100/(10)2] = 11 Ω

Test: Equivalent Circuit of Transformer - Question 2

Find the transformer ratios a and b that the impedance Zin is resistive and equal to 2.5 Ω when the network is excited with a sine wave voltage of angular frequency of 5000 rad/s

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 2

Concept:

Referred value in Transformer:

In order to simplify the calculation, it is theoretically possible to transfer the voltage, current, and impedance of one winding to the other winding and combined them to a single value for each quantity.

Considered a transformer has turns ration 'a' which is given by,

Where,

Iand I2 are primary and secondary current respectively.

V1 and V2 are primary and secondary voltage respectively.

Nand Nare numbers of turn in primary and secondary respectively.

For an ideal transformer:

Input Power = Output Power

Equivalent secondary Impedance in terms of primary Impedance:

Equivalent primary Impedance in terms of secondary Impedance:

Calculation:

Given,

Zin is resistive and equal to 2.5 Ω

Angular frequency ω = 5000 rad/s

 

Inductive reactance XL = jωL = j 5000 × 1 × 10-3 = j 5 Ω 

Capative reactance XC = 1 / jωC = 1 / j(5000 × 10 × 10-6) = - j 20 Ω 

The input impedance of the transformer from the secondary side of the transformer will be

Z' = XL + R/a2 = j 5 + 2.5/a2

Circuit diagram will be as follows  

The input impedance of the transformer from the primary side of the transformer will be

It is given that the input impedance is resistive, therefore there won't be any reactance term in the input impedance

As there is no reactance in the input impedance, make reactance equal to zero in the above equation

Now the given resistive term of the input impedance is equal to 2.5 Ω 

Therefore the value of a = 2.0, b = 0.5 

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Test: Equivalent Circuit of Transformer - Question 3

A one-phase, 50 Hz, 40 kVA transformer with a ratio of 2000 V/250 V has a primary resistance of 1.15 Ω and a secondary resistance of 0.0155 Ω. Calculate total copper loss on half of the full load. 

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 3

Concept:

Consider a two winding single phase transformer as shown below,

N1 = primary winding turns

N2 = secondary winding turns

V1 = primary winding voltage

V2 = secondary winding voltage

I1 = current through the primary winding

I2 = current through the secondary winding

Transformation ratio: It is defined as the ratio of the secondary voltage to the primary voltage. It is denoted by K.

Transformer equivalent circuit with respect to secondary can be represented a show below

Where R02 = Effective resistance of the transformer as referred to the secondary side of the transformer.

R02 = R2 + R1'    ------- (2)

R1' = Equivalent primary resistance as referred to the secondary winding

R1' = R× K 2  ------ (3)

Similarly, effective resistance of the transformer as referred to the primary side of the transformer is given as,

R01 = R1 + R2

R2' = Equivalent secondary resistance as referred to the primary winding

R2' = R2 / K 2

Calculation:

Given data

V1 = 2000 V, V2 = 250 V, R1 = 1.15 Ω, R2 = 0.0155 Ω

From equation(1)

K= V2 / V1

K = 250 / 2000

K = 1 / 8

Effective resistance of the transformer as referred to the secondary of the transformer.

From equations(2) & (3)

R02 = 0.0155 + 1.15 / 82

R02 = 0.0335 Ω

Power output P = 40 kVA

V2 I= 40 × 103

I2 = 40000 / 250

I2 = 160 A = Ifl

Ifl is the full load current flowing through the secondary.

We required to find power loss at half full load condition

So, current at half full load is given as,

∴ Total power loss at half full load condition is given as,

Phfl = I2hfl × R02

Phfl = 802 × 0.0335

Phfl = 214.2 W

Test: Equivalent Circuit of Transformer - Question 4

A 4000 V/2000 V, 60 Hz single phase transformer has a total impedance of 60 Ω referred to the primary side. The primary and secondary windings have negligible resistances. If the transformer supplies a resistive of 20 Ω, the full load voltage at the secondary side will be

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 4

Concept:

Consider a two winding single phase transformer as shown below,

N1 = primary winding turns

N2 = secondary winding turns

V1 = primary winding voltage

V2 = secondary winding voltage

I1 = current through the primary winding

I2 = current through the secondary winding

Transformation ratio: It is defined as the ratio of the secondary voltage to the primary voltage. It is denoted by k.

K=N2N1=V2V1=I1I2" tabindex="0">K=N2N1=V2V1=I1I----- (1)Transformer equivalent circuit with respect to secondary can be represented a show below

Where R02 = Effective resistance referred to the secondary side of the transformer.

R02 = R2 + R1' ........ (2)

R1' = Primary winding resistance as referred to the secondary side.

R1' = R1 × k2 ......... (3)

Similarly, the effective resistance referred to the primary side of the transformer is given as,

R01 = R1 + R2' 

R2' = Secondary winding resistance as referred to the primary side.

R2' = R2 / k2

Calculation:

 

Given total impedance of the transformer referred to primary R01 = 60 Ω 

Transformation ratio k = V2 / V1 = 2000 / 4000 = 0.5

Total impedance of the transformer referred to secondary when primary and secondary windings have negligible resistances is given as

R02 = R01 × k2

= 60 / 4 = 15 Ω

Apply the voltage division rule to find voltage across the load

VL = 2000 × 20 / (15 + 20)

VL = 1143 V

Test: Equivalent Circuit of Transformer - Question 5

The magnetisation branch of an equivalent circuit of a transformer is drawn in ________ with supply voltage.

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 5

Concept:

The equivalent circuit of the transformer is

I1 = Primary winding current

I2 ' =Secondary winding current referred to the primary side

I= NO - load current

I= Core loss component

I= magnetizing component No-load current is almost the same when we apply the load also.

The magnetizing branch circuit is connected in parallel to the supply voltage as the No-load current is constant while we apply load also. Therefore Core loss is also constant as Iremains constant

Test: Equivalent Circuit of Transformer - Question 6

For matching a circuit of output impedance 200 ohms with a load of 8 ohms, the turns ratio of the two winding of transformer should be

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 6

Concept:

Transformers are used for impedance matching applications. This is explained with the help of the following figure:

The load impedance reflected on the primary side is redrawn as shown:

For the load to match with the source resistance:

Calculation:

With RL = 8 Ω, and RS = 200 Ω, the transformation ratio will be:

Test: Equivalent Circuit of Transformer - Question 7

The single phase converter has a full load secondary current of 200 A, while the primary current is one-tenth of this value. Its primary resistance and secondary winding resistances are 1.5 Ω and 0.015 Ω, respectively. The leakage reactance values of the primary and secondary windings are 2 Ω and 0.02 Ω respectively. Which primary voltage will transmit the full load current through a short-circuit secondary, not neglecting the load current?

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 7

Calculation:

Given:

Primary resistance of Transformer R1 = 1.5 Ω

The primary reactance of Transformer X1 = 2j Ω

Secondary resistance of Transformer R2 = 0.015 Ω

Secondary reactance of Transformer X2 = 0.02j Ω

Primary Current I1 = 20 A

Secondary Current I2 = 200 A

Let Primary Induced Emf and Secondary Induced Emf be E1 and E2

Let primary Voltage be V1

Circuit Diagram Shown:

E2 = 200 (0.015 + j0.02)

E= 5∠ 53.13

Turns ratio (N) is given by

Now, by Applying KCL in Primary Circuit

Test: Equivalent Circuit of Transformer - Question 8

Which of the following is the correct mathematical relationship that connects primary and secondary parameters of a transformer?

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 8

Concept:

Consider a two winding single phase transformer as shown below,

N1 = primary winding turns

N2 = secondary winding turns

V1 = primary winding voltage

V2 = secondary winding voltage

I= current through the primary winding

I2 = current through the secondary winding

Transformation ratio: It is defined as the ratio of the secondary voltage to the primary voltage. It is denoted by k.

Test: Equivalent Circuit of Transformer - Question 9

Which of the following is the correct mathematical relationship that connects primary and secondary parameters of a transformer?

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 9

Concept:

Consider a two winding single phase transformer as shown below,

N1 = primary winding turns

N2 = secondary winding turns

V1 = primary winding voltage

V2 = secondary winding voltage

I= current through the primary winding

I2 = current through the secondary winding

Transformation ratio: It is defined as the ratio of the secondary voltage to the primary voltage. It is denoted by k.

Test: Equivalent Circuit of Transformer - Question 10

In a single phase transformer the primary induced and secondary induced voltage vectors are-

Detailed Solution for Test: Equivalent Circuit of Transformer - Question 10

Concept:

Working of Transformer on No load:

I1 = Supply current

I2 = Load current

I'2 = Load current reflected on the primary

I0 = No-load current

When the transformer is operating at no-load condition, the load current (I2) on the secondary side is zero. Since Iis zero, its reflected current on the primary side (I'2) is also zero. 

Supply current Iis the sum of no-load current (I0) and load current reflected on the primary side (I'2). 

Means supply current is no-load current itself

No-Load current has two components:

Active or power component (Ii): The active component of the no-load current is always in phase with supply voltage (V1) and is responsible for iron losses.

Magnetizing component (Im): The magnetizing component of the no-load current is responsible for flux production in the core of the transformer, hence it is out of phase with supply voltage (V1) or in phase with flux (ø).

Phasor diagram:

 

  • The active component of the no-load current is always in phase with supply voltage (V1).
  • The magnetizing component of the no-load current is responsible for flux production in the core of the transformer, hence it is in phase with flux (ø).
  • Induced emf in the primary winding (E1) lags the flux ø by 90 degrees.
  • The applied voltage (V1) is equal and opposite to the induced emf on the primary side (E1) as losses on the primary side are negligible because the no-load current is 5% to 8% of the rated current. 

From Turns Ratio:

where, N1 = No. of turns on the primary side

N2 = No. of turns on the secondary side

E1 = EMF induced on the primary side

E= EMF induced on the secondary side

 Therefore, from the above phasor diagram, it is clear that the induced voltage in the primary and secondary induced windings of the transformer are in the same phase.

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