Thursday, 26 March 2015

electromagnetic induction - Secondary current in a loosely coupled transformer


How does the secondary current depend on the resistive load placed on the secondary winding of a loosely coupled transformer, in which the primary winding is supplied with a linear current ramp ?



Answer




The easiest way to analyze such problem is to write Kirchhoff's equations for a pair of coupled coils, the way EEs do it: V1=L1dI1dt+MdI2dtV2=MdI1dt+L2dI2dt

with the termination condition : V2=I2R2


You have also specified that the input current is a ramp I1=k1t so that the coupled equations become V1=L1k1+MdI2dtI2R2=Mk1+L2dI2dt

and after rearrangement L2dI2dt+I2R2+Mk1=0 for t>0 the solution of which is an increasing exponential I2(t)=Mk1R2(1etR2L2). Notice that this approaches a constant current Imax=Mk1R2 as t


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