ELEC 273 Mid-Term Test Name:__________________________ October 20, 2018 from 14:00 until 15:30. I.D. #:__________________________ Instructors: C.W. Trueman, F. Fayyaz Instructions Closed book exam: no notes or books are allowed. Calculator: You are permitted to have a calculator with an ENCS sticker. No other calculator is allowed. Return the exam paper with your answer booklet. You must NOT have a cell phone or other electronic device in your possession.

Figure 1(a)

1.(a) For the circuit in Figure 1(a), using the branch currents 𝑖𝑖1, 𝑖𝑖2, 𝑖𝑖3 and 𝑖𝑖4 as unknowns, write two KCL equations and two KVL equations that can be solved for the values of the branch currents. (6 marks) Note: you are not permitted to write node equations or mesh equations to answer this question.

Figure 1(b)

1.(b) For the circuit in figure 1b, find the input resistance 𝑅𝑅𝑖𝑖𝑖𝑖. (4 marks)

Figure 2

2.(a) Write a set of node equations for the circuit in Figure 2. (8 marks) 2.(b) Arrange your equations into matrix form. (2 marks)

Figure 3

3.(a) Write a set of mesh equations for the circuit in Figure 3. (6 marks) 3.(b) Solve the mesh equations to find the values of the mesh currents. (2 marks) 3.(c) For the circuit in Figure 3, find the voltage across the current source. Does the current source deliver power to the circuit or absorb power from the circuit? (2 marks)

Figure 4

4.(a) Find the Thevenin equivalent at terminals a b for the circuit in Figure 4. (6 marks) 4.(b) Connect a 3Ω load resistor RL across terminals a and b in Figure 4. Use the Thevenin Equivalent circuit to find the voltage 𝑉𝑉𝑎𝑎𝑎𝑎 across RL. Is 𝑉𝑉𝑎𝑎𝑎𝑎 positive or negative? (2 marks) 4.(c) What value of RL absorbs the maximum amount of power? With this value of RL how much power does RL absorb? (2 marks)

Solution to the ELEC 273 Mid-Term Test October 20, 2018

Figure 1(a)

1.(a) For the circuit in Figure 1(a), using the branch currents 𝑖𝑖1, 𝑖𝑖2, 𝑖𝑖3 and 𝑖𝑖4 as unknowns, write two KCL equations and two KVL equations that can be solved for the values of the branch currents. (6 marks) Note: you are not permitted to write node equations or mesh equations to answer this question.

Solution: 1.(a)

1.(b) For the circuit in figure 1b, find the input resistance 𝑅𝑅𝑖𝑖𝑖𝑖. (4 marks)

Figure 1(b)

Alternate solution using star-delta transformation:

Alternate solution using delta-star transformation:

Figure 2

2.(a) Write a set of node equations for the circuit in Figure 2. (8 marks) 2.(b) Arrange your equations into matrix form. (2 marks)

Alternate solution with four nodes:

Figure 3

3.(a) Write a set of mesh equations for the circuit in Figure 3. (6 marks) 3.(b) Solve the mesh equations to find the values of the mesh currents. (2 marks) 3.(c) For the circuit in Figure 3, find the voltage across the current source. Does the current source deliver power to the circuit or absorb power from the circuit? (2 marks)

Solve the equations:

Let 𝑉𝑉𝑠𝑠 be the voltage across the current source.

The current source delivers power to the circuit.

Figure 4

4.(a) Find the Thevenin equivalent at terminals a b for the circuit in Figure 4. (6 marks) 4.(b) Connect a 3Ω load resistor RL across terminals a and b in Figure 4. Use the Thevenin Equivalent circuit to find the voltage 𝑉𝑉𝑎𝑎𝑎𝑎 across RL. Is 𝑉𝑉𝑎𝑎𝑎𝑎 positive or negative? (2 marks) 4.(c) What value of RL absorbs the maximum amount of power? With this value of RL how much power does RL absorb? (2 marks)

4.(a) Find the Thevenin Equivalent Circuit Find the open circuit voltage:

Find the short circuit current:

Check with the dead-circuit method:

The Thevenin Equivalent Circuit: (note the polarity of the source)

4.(b) Find the voltage across a load of 3 ohms.

4.(c) Choose the load resistor to be equal to the Thevenin Equivalent Resistance: