Question 2014.S3.40: The parameters measured for a 220 V/110 V, 50 Hz, single-pha......
The parameters measured for a 220 V/110 V, 50 Hz, single-phase transformer are:
Self-inductance of primary winding = 45 mH
Self-inductance of secondary winding = 30 mH
Mutual inductance between primary and secondary windings = 20 mH
Using the above parameters, the leakage (L_{l1},~L_{l2}) and magnetising \left(L_{ m }\right) inductances as referred to primary side in the equivalent circuit respectively, are
(a) 5 mH, 20 mH and 40 mH
(b) 5 mH, 80 mH and 40 mH
(c) 25 mH, 10 mH and 20 mH
(d) 45 mH, 30 mH and 20 mH
Given that V_1=220 V , V_2=110 V f=50 Hz , L_1=45 mH , L_2=30 mH , M=20 mH
Leakage inductance,
\begin{aligned}& L_{ l1 }=L_1-2 M=45-20(2)=5 mH \\ & L_{12}=L_2-2 M=30-2(20)=10 mH \end{aligned}
L_{l2} as referred to primary side is
L_{12}^{\prime}=\frac{30}{(1 / 2)^2}=2(20)=120-40=80 mH
Magnetising inductance with reference to primary is given by
L_{ m }=k L_1
where k is the coupling coefficient.