EE221 Circuits II Instructor: Prof.
Yingtao Jiang
1. For the three coupled coils below, calculate the total inductance.
Solution:
2. Two coils connected in series-aiding fashion have a total inductance of 250mH. When connected in a series-
opposing configuration, the coils have a total inductance of 150mH. If the inductance of one coil (L1) is
three times the other, find L1, L2, and M. What is the coupling coefficient?
Solution:
3. Two coils are mutually coupled, with 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.
Solution:
(a)
(b)
4. For the circuit below, find 𝑉𝑜 .
EE221 Circuits II Instructor: Prof. Yingtao Jiang
Solution:
5. Determine the equivalent Leq in the circuit below.
Solution:
EE221 Circuits II Instructor: Prof. Yingtao Jiang
We can also use the equivalent T-section for the transform to find the equivalent inductance.
6. Obtain the Thevenin equivalent circuit for the circuit in the following circuit at terminals a-b.
Solution:
EE221 Circuits II Instructor: Prof. Yingtao Jiang
7. Find the Thevenin equivalent to the left of the load Z in the following circuit.
Solution:
EE221 Circuits II Instructor: Prof. Yingtao Jiang
8. Determine an equivalent T-section that can be used to replace the transformer in the following circuit.
Solution:
Thus, the T-section is shown as the upper-right.
EE221 Circuits II Instructor: Prof. Yingtao Jiang
9. If M = 0.2 H and 𝑣𝑠 = 12cos10t V in the following circuit, find 𝑖1 and 𝑖2 . Calculate the energy stored in the
coupled coils at t = 15ms.
Solution:
EE221 Circuits II Instructor: Prof. Yingtao Jiang
10. In the circuit below, (a) find the coupling coefficient, (b) calculate 𝑣𝑜 , (c) determine the energy stored in the
coupled inductors at 𝑡 = 2𝑠.
Solution:
EE221 Circuits II Instructor: Prof. Yingtao Jiang
11. Find 𝑍𝑎𝑏 and 𝐼𝑜 for the following network.
Solution:
12. Find the average power delivered to the 50Ω resistor in the following circuit.
Solution:
We apply mesh analysis to the circuit as shown below.
EE221 Circuits II Instructor: Prof. Yingtao Jiang
Use the Matlab or other tools, or calculate it by hand,
13. In the following circuit, find the value of the coupling coefficient k that will make the 10-Ω resistor
dissipate 320 W. For this value of k, find the energy stored in the coupled coils at t = 1.5 s.
Solution:
EE221 Circuits II Instructor: Prof. Yingtao Jiang
EE221 Circuits II Instructor: Prof. Yingtao Jiang
14. Determine the input impedance of the following air-core transformer circuit.
Solution:
15. A 480/2,400-V rms step-up ideal transformer delivers 50 kW to a resistive load. Calculate:
(a) the turns ratio,. (b) the primary current, (c) the secondary current.
Solution:
16. Determine𝐼1 and 𝐼2 in the following circuit.
Solution:
17. For the circuit shown below, find the value of the average power absorbed by the 8-Ω resistor.
EE221 Circuits II Instructor: Prof. Yingtao Jiang
Solution:
We now have some choices, we can go ahead and calculate the current in the second loop and calculate the
power delivered to the 8-ohm resistor directly or we can merely say that the power delivered to the equivalent
resistor in the primary side must be the same as the power delivered to the 8-ohm resistor. Therefore,
You can calculate the current in the secondary and calculate the power delivered to the 8-ohm resistor to verify
that the above is correct.
18. Find current 𝑖𝑥 in the ideal transformer circuit shown below.
Solution:
EE221 Circuits II Instructor: Prof. Yingtao Jiang
19. Refer to the circuit below: (a) find currents 𝐼1 , 𝐼2 and 𝐼3 , (b) Find the power dissipated in the 40-Ω resistor.
Solution:
(a) Transferring the 40-ohm load to the middle circuit,
20. Find the mesh currents in the following circuit.
EE221 Circuits II Instructor: Prof. Yingtao Jiang
Solution:
21. A 240/120-V rms power transformer is rated at 10 kVA. Determine the turns ratio, the primary current, and
the secondary current.
Solution:
