Electrical Engineering / Tutorial
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T.3.
Magnetically Coupled Circuits
T.3.1 Problems
Problem 1
For the three coupled coils in the figure, calculate the total inductance.
10H
Problem 2
Two coils connected in series-aiding fashion have a total inductance of 250 mH. When connected in a
series-opposing configuration, the coils have a total inductance of 150 mH. If the inductance of one
coil (L1) is three times the other, find L1, L2, and M. What is the coupling coefficient?
150mH; 50mH; 25mH; 0.29
Problem 3
Two coils are mutually coupled. L1 = 25 mH, L2 = 60 mH, and k = 0.5. Calculate the maximum possible
equivalent inductance if:
(a) the two coils are connected in series,
(b) the coils are connected in parallel.
123.7mH; 24.31mH
Problem 4
The coils in the figure have L1 = 40 mH, L2 = 5 mH,
and coupling coefficient k=0.6.
Find i1 (t) and v2 (t) given that
=
v1 (t ) 10 cos=
ωt and i2 (t ) 2sin
=
ωt , ω 2000 rad/s.
0.55sin(ωt)A; 22.1cos(ωt+25°)V
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Michael E. Auer
Carinthia University of Applied Sciences
Electrical Engineering / Tutorial
2
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Problem 5
Find v(t) for the circuit below.
v(t) = 24.25cos(4t–14.03˚) V
Problem 6
In the circuit, ZL is a 15-mH inductor having an impedance of j40 Ω.
Determine Zin when k=0.6.
13.073 + j25.86 Ω
Problem 7
A 4800-V rms transmission line feeds a distribution transformer with 1200 turns on the primary and 28
turns on the secondary. When a 10-Ω load is connected across the secondary, find:
(a) the secondary voltage,
(b) the primary and secondary currents,
(c) the power supplied to the load.
112V; 261mA; 11.2mA; 1254W
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Michael E. Auer
Carinthia University of Applied Sciences