EQUIVALENT RESISTANCE

Figure 1.26 Individual Resistances

Figure 1.26 shows a transformer having primary resistance R₁ and secondary resistance R₂, where resistances have been shown external to the wind-ings. In Figure 1.26, it is assumed that there is no fringing, i.e. no leakage of flux. It is possible to transfer resistance from one winding to another to simplify the calculation. Let N₁ and N₂ be the number of turns of primary and secondary winding respectively. Let the turns ratio be ‘a’. Let I₁ and I₂ be the currents in primary and secondary winding, respectively. Neglecting I₀, = a. Let the referred value of R₂ be R₂^′ when it is transferred to primary. The copper loss of secondary is I₂²R₂ when R₂ is in secondary. The copper loss across R₂^′ is I₁²R₂^′ when R₂ has been transferred to primary. These two losses must be equal.

∴ I₂²R₂=I₁²R₂^′

i.e.,

The total resistance referred to as primary becomes R₁ + R₂^′ or R₁ + a²R₂. This is also known as equivalent or effective resistance of the transformer referred to as primary and is denoted by R₀₁.

R₀₁=R₁+a²R₂ (1.13)

Figure 1.27 is the equivalent of Figure 1.26 when the secondary resistance is transferred to the primary.

If R₁ is transferred to secondary, having referred value R₁^′, we have

I₁²R₁=I₂²R₁^′

i.e.,

Figure 1.27 Resistance Referred to as Primary

Therefore, the equivalent resistance of the transformer referred to as secondary becomes

Figure 1.28 is the equivalent of Figure 1.26 when the primary resistance is trans-ferred to the secondary.

Figure 1.28 Resistance Referred to as Secondary

Figure 1.29 Magnetic Leakage and Equivalent Circuit