Derive the emf equation of single phase transformer

Transformer’s EMF Equation Magnitude of the induced EMF (or Voltage) in a EMF equation of the transformer. When a source of alternating current (AC) is applied to the primary winding of the transformer which is known as magnetizing current, it produces alternating flux in the core of a transformer. The produced alternating mutual induction as it is alternating flux in nature, there must be a rate of change of flux according to Faraday’s law of electromagnetic induction which states that if a conductor or coil links with any changing flux, there must be an induced emf in it. The same happens in • Also read: EMF Equation of Electrical Transformer Now let’s know how to find the magnitude of the induced EMF in a transformer by the EMF equation of the transformer. Lets, • N 1= Number of turns in primary windings. • N 2 = Number of turns in second windings. • Φ m= Maximum flux in the core in Weber = ( Φ m = B m .A) • f = Frequency of A.C input in H z. Related Post: As shown in fig above- flux increases from its zero value to maximum value Φ m in one quarter of the cycle i.e. in ¼ second. Average rate of change of flux = [ Φ m / ( ¼ f.)] = 4 f Φ m Wb/s or volt The constant “K” is known as voltage transformation ratio. • If N 2> N 1, i.e. K > 1, then the transformer is known as a step-up transformer. • If N 2< N 1, i.e. K < 1, then the transformer is called step-down transformer. Where, N 1= Primary number of turns of the coil in a transformer. N 2 = Secondary number of turns. • Y...

Figure 1.22 shows the representation of alternating flux, varying sinusoidally, which increases from its zero value to maximum value ( Φ m) in one-quarter of the cycle, that is in one-fourth of a second where fis the frequency of AC input in hertz. The average rate of change of flux is given by , that is 4 fΦ m Wb/s or V. where is the maximum value of flux density having unit Tesla (T) and A r is the area of cross-section. Similarly, RMS value of induced emf in secondary winding is E 2 = (4.44 f Φ m )x N 2 = 4.44 fΦ m N 2 = 4.44 f B mA rN 2 (1.2) From Equations (1.1) and (1.2), we have i.e., where ‘ a’ is the turns ratio of the transformer, i.e., Equation (1.3) shows that emf induced per turn in primary and secondary windings are equal. In an ideal transformer at no load, V 1 = E 1 and V 2 = E 2, where V 2 is the terminal voltage of the transformer. Equation (1.3) becomes Example 1.1 The voltage ratio of a single-phase, 50 Hz transformer is 5,000/500 V at no load. Calculate the number of turns in each winding if the maximum value of the flux in the core is 7.82 mWb. Solution Here E 1 = V 1 = 5,000 V E 2 = V 2 = 500 V φ max = 7.82 m Wb = 7.82 × 10 −3 Wb, f = 50Hz Let N 1 and N 2 be the number of turns of the primary and secondary windings, respectively. Since E 1 = 4.44 f φ m N 1 i.e., Again, ∴

Emf Equation of Transformer EMF Equation of transformer can be established in a very easy way. Actually in As the emf equation of transformer. Let’s say, T is number of turns in a winding, Φ m is the maximum flux in the core in Wb. As per Where φ is the instantaneous alternating flux and represented as, As the maximum value of cos2πft is 1, the maximum value of induced emf e is, To obtain the rms value of induced counter emf, divide this maximum value of e by √2. This is the EMF equation of transformer. If E 1 & E 2 are primary and secondary emfs and T 1 & T 2 are primary and secondary turns then, turns ratio of transformer is, Transformation Ratio of Transformer This constant is called transformation ratio of transformer , if T 2>T 1, K > 1, then the transformer is step up transformer. If T 2< T 1, K < 1, then the transformer is step down transformer. Voltage Ratio of Transformer This above stated ratio is also known as voltage ratio of transformer if it is expressed as ratio of the primary and secondary voltages of transformer. Turns Ratio of Transformer As the voltage in primary and secondary of transformer is directly proportional to the number of turns in the respective winding, the transformation ratio of transformer is sometime expressed in ratio of turns and referred as turns ratio of transformer .

For electrical transformer, the EMF equation is a mathematical expression used to find the magnitude of induced EMF in the windings of the transformer. Consider a transformer as shown in the figure. If N 1 and N 2 are the number of turns in primary and secondary windings. When we apply an alternating voltage V 1 of frequency f to the primary winding, an alternating magnetic flux $\phi$ is produced by the primary winding in the core. If we assume sinusoidal AC voltage, then the magnetic flux can be given by, $$\mathrm$$ It is not possible for a winding to have part of a turn. Thus, the number of turns should be a whole number.