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Equivalent Resistance Formula

Find the equivalent resistance between a and b

Both the coils of the transformer have resistance. There is no electrical connection between the coils. Theoretically, the resistance of one circuit is transferred to another circuit in an equivalent manner. As a result, all the calculations can be done very easily in an extraordinary way. Because in this case, only one circuit has to be calculated Both circuits do not require a long and complex process.

This is why the resistance of any one circuit is transferred to another circuit in the same way. Needless to say, the transfer process is theoretically impossible.

The winding resistance of a transformer is usually indicated in three ways Namely: - 

1. The correct resistance of both windings is displayed in both windings

2. Display the total resistance of both windings in secondary without displaying in primary

3. The total resistance of the winding is not displayed in the secondary but in the primary 


Transferred to the transformer primary equivalent resistance:

As we know,

the primary coil resistive drops = IpRp

secondary coil resistive drop= IsRs

primary to secondary coil resistive drop  = transformation ratio (Is.a.Rs)

in the primaries of the resistive drop in both the quail: 

=IpRp + IsRs . a

= IpRp + Ip.a.Rs.a

=Ip(Rp + Rs a2)

=IpRe'

Here,

Re'= equivalent resistance to the primary .

Transferred to the secondary transformer equivalent resistance: -

As we know, 

the secondary coil resistive drops = IsRs

the primary coil resistive drops = IpRp


secondary in the context of the primary quail resistive drops =IpRp/a

both coil to the secondary total of resistive drop=

=IsRs + IpRp/a
=IsRs + IsRs/a2
=Is (Rs + Rp/a2)
= IsRe"

here,

Re" = equivalent resistance to the Secondary .


Note that

  1.  when the secondary resistance is transferred to the primary, the secondary resistance has to be multiplied by the transformation ratio square a2.

  2. When the primary resistance is transferred to the secondary key, the primary resistance has to be divided by the transformation ratio square a2.

  3. The transformation ratio will also be used when voltage is transferred from one winding to another winding. 

For example: - 

 We know, Vp / Vs = a or Vp = Vs.a i.e. multiplying the secondary voltage by the ratio a becomes equal to the primary voltage.


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