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- Basic Concepts
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- Energy Stored in a Magnetic Field
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- Faraday’s Laws of Electromagnetic Induction
- Concept of Induced EMF
- Fleming’s Left Hand and Right Hand Rules
- Transformers
- Electrical Transformer
- Construction of Transformer
- EMF Equation of Transformer
- Turns Ratio and Voltage Transformation Ratio
- Ideal and Practical Transformers
- Transformer on DC
- Losses in a Transformer
- Efficiency of Transformer
- Three-Phase Transformer
- Types of Transformers
- DC Machines
- Construction of DC Machines
- Types of DC Machines
- Working Principle of DC Generator
- EMF Equation of DC Generator
- Types of DC Generators
- Working Principle of DC Motor
- Back EMF in DC Motor
- Types of DC Motors
- Losses in DC Machines
- Applications of DC Machines
- Induction Motors
- Introduction to Induction Motor
- Single-Phase Induction Motor
- Three-Phase Induction Motor
- Construction of Three-Phase Induction Motor
- Three-Phase Induction Motor on Load
- Characteristics of 3-Phase Induction Motor
- Speed Regulation and Speed Control
- Methods of Starting 3-Phase Induction Motors
- Synchronous Machines
- Introduction to 3-Phase Synchronous Machines
- Construction of Synchronous Machine
- Working of 3-Phase Alternator
- Armature Reaction in Synchronous Machines
- Output Power of 3-Phase Alternator
- Losses and Efficiency of 3-Phase Alternator
- Working of 3-Phase Synchronous Motor
- Equivalent Circuit and Power Factor of Synchronous Motor
- Power Developed by Synchronous Motor
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Turns Ratio and Voltage Transformation Ratio
As discussed in the previous chapter, the EMF of equation of a transformer is given by,
$$\mathrm{\mathit{E}\:=\:4.44\:\mathit{f\phi _{m}\:N}}$$
For primary winding,
$$\mathrm{\mathit{E_{\mathrm{1}}}\:=\:4.44\:\mathit{f\phi _{m}\:N_{\mathrm{1}}}\:\cdot \cdot \cdot (1)}$$
For secondary winding,
$$\mathrm{\mathit{E_{\mathrm{2}}}\:=\:4.44\:\mathit{f\phi _{m}\:N_{\mathrm{2}}}\:\cdot \cdot \cdot (2)}$$
Turns Ratio of Transformer
From equations (1) and (2), we have,
$$\mathrm{\frac{\mathit{E_{\mathrm{1}}}}{\mathit{E_{\mathrm{2}}}}\:=\:\frac{\mathit{N_{\mathrm{1}}}}{\mathit{N_{\mathrm{2}}}}\:=\mathrm{a}\:\:\cdot \cdot \cdot (3)}$$
The constant "a" is known as the turns ratio of the transformer. It may be defined as under,
The ratio of number of turns in the primary winding the number of turns in the secondary winding of a transformer is known as turns ratio.
Voltage Transformation Ratio of Transformer
The ratio of output voltage to the input voltage of transformer is known as voltage transformer ratio, i.e.,
$$\mathrm{\mathrm{Transformation\: Ratio}\:=\:\frac{Output \:Voltage}{Input \:Voltage}}$$
Thus, if V1 is the input voltage and V2 is the output voltage of a transformer, then its transformation ratio is given by,
$$\mathrm{\mathrm{Transformation\: Ratio}\:=\:\frac{\mathit{V_{\mathrm{2}}}}{\mathit{V_{\mathrm{1}}}}\:\cdot \cdot \cdot (4)}$$
For an ideal transformer, V1 = E1 and V2 = E2, then
$$\mathrm{\mathrm{Transformation\: Ratio}\:=\:\frac{\mathit{V_{\mathrm{2}}}}{\mathit{V_{\mathrm{1}}}}\:=\:\frac{\mathit{E_{\mathrm{2}}}}{\mathit{E_{\mathrm{1}}}}\:=\:\:\frac{\mathit{N_{\mathrm{2}}}}{\mathit{N_{\mathrm{1}}}}\:=\:\frac{1}{a}\cdot \cdot \cdot (5)}$$
However, in a practical transformer, there is a small difference between V1 and E1, and V2 and E2, due to winding resistances. Although, this difference is very small so for analysis purposes, we take V1 = E1 and V2 = E2.
Numerical Example (1)
A transformer with 1000 primary turns and 400 secondary turns is supplied from a 220 V AC supply. Calculate the secondary voltage and the volts per turn.
Solution
Given data,
$$\mathrm{\mathit{N_{\mathrm{1}}}\:=\:1000\:\mathrm{and}\:\mathit{N_{\mathrm{2}}}\:=\:400}$$
$$\mathrm{\mathit{V_{\mathrm{1}}}\:=\:220\:V}$$
The turns ratio of transformer is,
$$\mathrm{\frac{\mathit{V_{\mathrm{1}}}}{\mathit{V_{\mathrm{2}}}}\:=\:\frac{\mathit{N_{\mathrm{1}}}}{\mathit{N_{\mathrm{2}}}}}$$
$$\mathrm{\Rightarrow \mathit{V_{\mathrm{2}}}\:=\:\mathit{V_{\mathrm{1}}}\times \frac{\mathit{N_{\mathrm{2}}}}{\mathit{N_{\mathrm{1}}}}\:=\:220\times \frac{400}{1000}}$$
$$\mathrm{\therefore\mathit{V_{\mathrm{2}}}\:=\:88\:\mathrm{Volts}}$$
The volts per turn is given by,
$$\mathrm{\mathrm{For\: primary\: winding}\:=\:\frac{\mathit{V_{\mathrm{1}}}}{\mathit{N_{\mathrm{1}}}}\:=\:\frac{200}{1000}\:=\:0.22\:\mathrm{Volts}}$$
$$\mathrm{\mathrm{For\: Secondary\: winding}\:=\:\frac{\mathit{V_{\mathrm{2}}}}{\mathit{N_{\mathrm{2}}}}\:=\:\frac{88}{400}\:=\:0.22\:\mathrm{Volts}}$$
Hence, from this example, it is clear that the volts per turn for a transformer remain the same on both primary and secondary windings.
Numerical Example (2)
A transformer with an output voltage of 2200 V is supplied at 220 V. If the secondary winding has 2000 turns, then calculate the number of turns in primary winding.
Solution
Given data,
$$\mathrm{\mathit{V_{\mathrm{1}}}\:=\:200\:\mathit{V}\:\mathrm{and}\:\mathit{V_{\mathrm{2}}}\:=\:2200\:\mathit{V}}$$
$$\mathrm{\mathit{N_{\mathrm{2}}}\:=\:2000\:\mathrm{turns}}$$
The turns ratio of transformer is,
$$\mathrm{\frac{\mathit{V_{\mathrm{1}}}}{\mathit{V_{\mathrm{2}}}}\:=\:\frac{\mathit{N_{\mathrm{1}}}}{\mathit{N_{\mathrm{2}}}}}$$
$$\mathrm{\Rightarrow {\mathit{N_{\mathrm{1}}}}\:=\:\mathit{N_{\mathrm{2}}}\:\times \:\frac{\mathit{V_{\mathrm{1}}}}{\mathit{V_{\mathrm{2}}}}\:=\:\mathrm{2000}\:\times \:\frac{220}{2200}\:=\:\mathrm{200\:turns}}$$
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