Transformers MCQ Quiz - Objective Question with Answer for Transformers - Download Free PDF

Calculation:

An ideal transformer operates based on the principle that the ratio of the primary voltage (V_p) to the secondary voltage (V_s) is equal to the ratio of the number of turns in the primary winding (N_p) to the number of turns in the secondary winding (N_s)
Mathematically, this is expressed as:

For ideal transformer  V s /V p = N s /N p

\(\frac{V_s}{V_p} = \frac{Ns}{Np} =\frac{2}{1}\)

∴ The correct option is 2)

Concept: 

To solve this problem, we need to use the transformer voltage ratio formula:

\(\frac{V_p}{V_s} = \frac{N_p}{N_s}\)

Where

V_p is the primary voltage,

V_s  is the secondary voltage,

Np is the number of turns in the primary coil,

N_s is the number of turns in the secondary coil.

Calculation: 

⇒ V_s = \(V_p × \frac{N_s}{N_p}\) = 220 × 10/100 =22 V

The secondary coil is connected to two resistances in series: 15 kΩ and 7 kΩ.

The total resistance is:

⇒ R_total = 15 + 7 = 22 kΩ

Since the total resistance is in series and the secondary voltage is 22 V, the output voltage across the 7 kΩ resistor can be calculated using the voltage division rule:

V_o = 22 × \(\frac{7}{22}\) = 7

∴ The output voltage (V0) is 7 V

Concept:

Transformer:

• Transformers are electrical devices consisting of two or more coils of wire used to transfer electrical energy using a changing magnetic field.
• The ratio of the output power to the input power in a transformer is known as the efficiency of the transformer. 

η = Output Power(Pi)/(Vp) Input Power

• The power of an electric circuit is calculated by multiplying the voltage by the current intensity.
• The value of the power in the primary is the same as the power in the secondary, as in the case of a transformer.
• η = (V_s × I_s) / (V_p × I_p)
• Where Vs, and Is are voltage and current in the secondary coil. Vp, Ip are the voltage and current in the primary coil.

Calculation:

Here, η = 80%, Pi = 4 KW = 4000W, Vp = 10 V, Vs = 240V

Since, Ip = Pi/Vp = 4000/10 = 400 A

Since, η = (Vs × Is) / (Vp × Ip)

⇒ 80/100 = (240 × Is) / (10 × 400)

⇒ I_s = 13.33 A

∴ Option 2) is the correct option

Explanation:

In a step-down transformer, the current is increased in the secondary circuit. This is because voltage and current are inversely proportional in a transformer, and a step-down transformer reduces the voltage while increasing the current to maintain power balance,

Concept:

Peak Current in an AC Circuit: The power consumed by an electrical device is given by:

• Formula: P = V_rms × I_rms
• Where:
  • P = Power (W)
  • V_rms = RMS voltage (V)
  • I_rms = RMS current (A)
• Peak current (I_m) is related to RMS current by:
• Formula: I_m = I_rms × √2

Calculation:

Given,

Power, P = 12 W

RMS Voltage, V_rms = 24 V

⇒ Using P = V_rms × I_rms

⇒ I_rms = P / V_rms

⇒ I_rms = 12 / 24

⇒ I_rms = 0.5 A

⇒ Peak current, I_m = I_rms × √2

⇒ I_m = 0.5 × 1.414

⇒ I_m ≈ 0.71 A

∴ The value of peak current (I_m) is 0.71 A.

CONCEPT:

Transformer:

• An electrical device that is used to transfer electrical energy from one electrical circuit to another is called a transformer.

There are two types of transformer:

1. Step-up transformer:

• The transformer which increases the potential is called a step-up transformer.
• The number of turns in the secondary coil is more than that in the primary coil.

2.Step-down transformer:

• The transformer which decreases the potential is called a step-down transformer.
• The number of turns in the secondary coil is less than that in the primary coil.

EXPLANATION:

• As in the step-up transformer, the number of coils in the secondary coil is more than that in the primary coil. So the electrical potential increases.
• Hence step-up transformer is used for increasing the voltage/potential. So option 4 is correct.

• In step-up transformer, the current in the secondary coil is less than that in the primary coil.

The correct answer is Minimize eddy current loss.

• Transformer cores are laminated in order to minimize core loss.
• By providing laminations, the area of each part gets reduced and hence resistance will get very high which limits the eddy current to a minimum value, and hence eddy current losses get reduced. 
• The laminations provide small gaps between the plates. As it is easier for magnetic flux to flow through iron than air or coil, the stray flux or leakage flux that can cause core losses is minimized.

CONCEPT:

Transformer:

An electrical device that is used to transfer electrical energy from one electrical circuit to another is called a transformer.

There are two types of transformer:

Step-up transformer:

• The transformer which increases the potential is called a step-up transformer.
• The number of turns in the secondary coil is more than that in the primary coil.

Step-down transformer:

• The transformer which decreases the potential is called a step-down transformer.
• The number of turns in the secondary coil is less than that in the primary coil.

EXPLANATION:

• As in the step-up transformer, the number of coils in the secondary coil is more than that in the primary coil. So the electrical potential increases.
• A step-up transformer converts low voltage at high current into a high voltage at low current. So option 4 is correct.

• In a step-up transformer, the current in the secondary coil is less than that in the primary coil.

• The secondary coil is made of thin insulated wire while the primary coil is made of thick insulated wire.

Concept:

• A transformer is an electrical device which transfers electrical energy from one circuit to another
• It works based on the principle of electromagnetic induction
• It is used for increasing or decreasing the amount of voltage or current as per our requirement based on these transformers are classified into two types step-up (increasing) or step-down (decreasing) transformer.

There are two types of transformer:

1. Step-up transformer:

• The transformer which increases the potential is called a step-up transformer.
• The number of turns in the secondary coil is more than that in the primary coil.

2.Step-down transformer:

• The transformer which decreases the potential is called a step-down transformer.
• The number of turns in the secondary coil is less than that in the primary coil.

Explanation:

As in an ideal transformer, there is no loss of power i.e.

Pout = Pin

So, VsIs = VpIp

\(\therefore \frac{{{V_s}}}{{{V_p}}} = \frac{{{N_s}}}{{{N_P}}} = \frac{{{I_P}}}{{{I_S}}}\)

Where Ns = number of turns of the secondary coil, NP = number of turns of the primary coil, Vs = Voltage secondary coil, VP = Voltage primary coil, Is = Current in the secondary coil and IP = current in the primary coil.

In Step up transformer voltage is increased So, the current will be reduced. As there is no loss in power.

Additional Information

• A transformer can be used to either increase or decrease the voltage of a circuit.
• In other words, it can either step up (increase) or step down (decrease) the voltage.
• A transformer is necessary because sometimes the voltage requirements of different appliances are variable.

CONCEPT:

• Transformer: A transformer is a device that is used to increase or decrease the supply voltage without a change in the frequency of AC current. The transformer works on the principles of electromagnetic induction and mutual induction.
• Types of transformer:
  1. ​​Step-up transformer: In this type of transformer the secondary output voltage is higher than the input voltage.
  2. Step down Transformer: In this type of transformer, the secondary output voltage is lower than the input voltage.

• The relationship between the primary and secondary turns in the transformer is given by

\(\Rightarrow \frac{V_{S}}{V_{P}} =\frac{N_{S}}{N_{P}} =\frac{I_{P}}{I_{S}}\)

V_s = Voltage in the secondary, V_p = Voltage in the primary, N_s= number of turns in the secondary circuit, N_p  = number of turns in the primary, I_P = Current in primary, and I_s = Current in secondary

CALCULATION :

Given N_P : N_s = 1 : 25

• The relationship between the current and the number of turns is given by

\(\Rightarrow \frac{I_{P}}{I_{S}} = \frac{N_{S}}{N_{P}}\)

Substituting the given values in the above equation

\(\Rightarrow I_{P} = \frac{N_{S}}{N_{P}} \times I_{s}\)

\(\Rightarrow I_{P} = \frac{25}{1} \times 2 = 50 A\)

• Hence, option 3 is the answer

CONCEPT:

• A Transformer is used to convert low voltage (or high current) to high voltage (or low current) and high voltage to low voltage.
  • It works on the principle of electromagnetic induction.
  • The primary coil has Np turns and the other coil, called the secondary coil, has Ns turns.
  • Generally, the primary coil works as the input coil and the secondary coil works as the output coil of the transformer.
• When an AC voltage is applied to the primary coil, the resulting current produces an alternating magnetic flux that links the secondary coil and induces an emf in it. The value of this emf depends on the number of turns in the secondary.

• In a transformer, the voltage in secondary is calculated by

\(\Rightarrow \frac{N_{s}}{N_{p}}=\frac{V_{s}}{V_{p}}=\frac{i_p}{i_s}\)
Where, Np and Ns are the numbers of turns in the primary and secondary coils respectively, Vp and Vs are the rms voltages across the primary and secondary respectively,  ip and is are the current in the primary and secondary coil.

• In a transformer, the load is connected to the secondary coil while the primary coil of a transformer is connected to an AC source.

EXPLANATION: 

Given - Np = 500, Ns = 200  and ip = 48 A

• The ratio of current in the primary and secondary coil is

\(\Rightarrow \frac{i_p}{i_s}=\frac{N_{s}}{N_{p}}\)

\(\Rightarrow i_s=i_p(\frac{N_p}{N_s})=48\times (\frac{500}{200})=120\, A\)

• Therefore option 3 is correct.

CONCEPT:

• Transformer: An electrical device that is used to transfer electrical energy from one electrical circuit to another is called a transformer.
  • In a transformer, there are two coils- The primary coil (P) and the secondary coil (S).
  • A Transformer is used to convert low voltage (or high current) to high voltage (or low current) and high voltage to low voltage.

There are two types of transformer:

• Step-up transformer: The transformer which increases the potential is called a step-up transformer.
  • The number of turns in the secondary coil is more than that in the primary coil.
• Step-down transformer: The transformer which decreases the potential is called a step-down transformer.
  • The number of turns in the secondary coil is less than that in the primary coil

As in an ideal transformer, there is no loss of power i.e.

Pout = Pin

So, VsIs = VpIp

\(\therefore \frac{{{V_s}}}{{{V_p}}} = \frac{{{N_s}}}{{{N_P}}} = \frac{{{I_P}}}{{{I_S}}}\)

Where Ns = number of turns of the secondary coil, NP = number of turns of the primary coil, Vs = Voltage secondary coil, VP = Voltage primary coil, Is = Current in the secondary coil, and IP = current in the primary coil.

EXPLANATION:

• In an ideal transformer, there is no loss of power.
• Hence option 3 is correct.

CONCEPT:

• A Transformer is used to convert low voltage (or high current) to high voltage (or low current) and high voltage to low voltage.

​

EXPLANATION:

• A Transformer is used to convert low voltage to high voltage and vice versa.
• This is done by changing the number of turns in primary and secondary coils.

In a transformer, the voltage in the secondary coil (load coil) is calculated by:

\(\frac{N_{s}}{N_{p}}=\frac{V_{s}}{V_{p}}\)
Here,Np and Ns are the numbers of turns in the primary and the secondary coils respectively and Vp and Vs are the rms voltages across the primary and secondary respectively.

• Transformers do not change AC current to DC current or vice versa.
• So the correct answer is option 2.

CONCEPT:

• Mutual induction: When an electric current is passed through a coil changes with time, an emf is induced in the nearby coil then this phenomenon is called mutual induction.

• Faraday's Laws of Electromagnetic Induction: Whenever the number of magnetic lines of force (magnetic flux) passing through a circuit/coil changes an emf is produced in the circuit called induced emf.

• Transformer: An electrical device that is used to transfer electrical energy from one electrical circuit to another is called a transformer.
  • In a transformer, there are two coils- Primary coil (P) and secondary coil (S).

• Both coils are electrically separate and inductive but are magnetically linked through the path of Reluctance.
• When the current in the primary coil is changed, the flux linked to the secondary coil also changes
• Consequently, an EMF is induced in the secondary coil due to Faraday laws of electromagnetic induction. 
• Electrical power transferred from the primary coil to secondary by magnetic flux and this phenomenon is called mutual induction.

EXPLANATION:

From the above explanation, can say that,

• The transformer transfers the electrical energy from one circuit to another.
• The working principle of the transformer is mutual induction. So option 2 is correct.
• Lorentz principle gives the force on a moving charged particle in a magnetic and electric field.
• Maxwell law is related to electromagnetic wave.
• Gauss law gives the electric flux through a closed surface.

EXTRA POINTS:

There are two types of transformer:

• Step-up transformer: The transformer which increases the potential is called a step-up transformer.
  • The number of turns in the secondary coil is more than that in the primary coil.
• Step-down transformer: The transformer which decreases the potential is called a step-down transformer.
  • The number of turns in the secondary coil is less than that in the primary coil

Concept:

Transformer:

• It is basically a voltage control device that is used widely in the distribution and transmission of alternating current power.
• A device used in the power transmission of electric energy.

• The transformer works on the principle of Faraday’s law of electromagnetic induction and mutual induction.
• In the transformer, \(\frac{N_1}{N_2}=\frac{I_2}{I_1}\), where N₁ and N₂ = the number of turns in the primary and secondary coil respectively, I₁ and I₂ = the current in the primary and secondary coil respectively.
• In terms of voltage, \(\frac{N_1}{N_2}=\frac{V_1}{V_2}\) where, N₁ and N₂ = the number of turns in the primary and secondary coil respectively, V₁ and V₂ = the voltage in the primary and secondary coil respectively.
   

​Half-wave rectifier:

• Half-wave rectifiers transform AC voltage to DC voltage.
• A halfwave rectifier circuit uses only one diode for the transformation.
• A halfwave rectifier is defined as a type of rectifier that allows only one-half cycle of an AC voltage waveform to pass while blocking the other half cycle. 
• 
• The DC output voltage, \(V_{DC}=\frac{V_m}{\pi}=\frac{\sqrt{2} V_2}{\pi}\)

Calculation:

Given,

The turns ratio of a transformer used in a half-wave rectifier is N1 ∶ N2 = 12 ∶ 1

The voltage at the primary coil, V₁ = 220 V

The frequency, f = 50 Hz

We know that, \(\frac{N_1}{N_2}=\frac{V_1}{V_2}\)

\(V_2=V_1\frac{N_2}{N_1}\)

\(V_2=220\times \frac{1}{12}=18.33 V\)

The DC output voltage is calculated as,  \(V_{DC}=\frac{V_m}{\pi}=\frac{\sqrt{2} V_2}{\pi}\)

\(V_{DC}=\frac{\sqrt{2} \times 18.33}{3.14}=8.255 V\)

Additional Information

• Faraday’s law of electromagnetic induction:
  • ​​Faraday’s Laws of Electromagnetic Induction consist of two laws.
  • Faraday's first law of electromagnetic induction: States Whenever a conductor is placed in a varying magnetic field, an electromotive force is induced
  • Faraday's second law of electromagnetic induction: States that the induced emf is equal to the rate of change in magnetic flux with respect to time.
  • Formula-induced emf, \(e=-N\frac{Δ ϕ}{Δ t}\) where N = number of turns, Δ ϕ = BAcosθ = Magnetic flux
• Mutual induction:
  • It is defined as the property of the coils that enables it to oppose the changes in the current in another coil.
  • With a change in the current of one coil, the flow changes too thus inducing EMF in the other coil