Question

Question 4 For the shown figure, assume that L1=3H, L2=4H, M=1H, i1(T)=1A and i2(T)=2A. M Primary Secondary + + A 12(t) i, (t) A v, (t) v (t) BO L L. Answer the following questions: a. Calculate the coupling coefficient (K)? b. Calculate the stored energy at t=T when the dot at position A? C. Calculate the stored energy at t=T when the dot at position B?

Answer 1

Solution) We are given the parameters, Primary in Secondary given 1,411 t AL Li=3H L2=4H m=1H to act) ylt) Valt) values 2, CT) = A (T)- 2A La calculation of Cu Coupling Now, for Coefficient CK). values thus, putting Sime K= m we ما را e get ki K= where, M= K= [3x4 = 0.2886 Ans 12 Mutual inductance K= coupling coeffident L = inductance of L2= inductance of ist will and coil Now, if dot is at A position then both the currents (idi) enters dot at same time astored thus Energy 2. 2 when dot wisse position Energy = 14,1² + 121 min А Stored at time I

- Thus, putting values, we get [x3x1? + Ix4x2 + 1X1X2 As. 11.5 Joules 1.5 + 8 + 2 = Now, if the dot is at position B then Currents enter and leave the dots at different time thus . 9 when dot at position B|Energy stored 2 7.5 Joules -x2 1² + 122 12² - mi,iz at time I x3x2 + 4x 4 xa? – IxIx 2 1.5 +8 - 2 duy Thus all the values were calculated out with proper answers & explanation Į
therefore all the values were calculated using the given values and proper formulae and detailed explanation was provided .