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Circuit Analysis: AC, Linear Circuits and Transients

In the circuit in the figure, E = 12 V, R1 = 4 Ω, R2 = 12 Ω and the current source is J = 2 A (flowing into node A). Which of the following is the voltage VA of node A with respect to ground?

DC circuit with a voltage source and a current source + E R1 A J R2
DC circuit with a voltage source and a current source · View in diagrams
  1. A6 V
  2. B9 V
  3. C15 V
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Answer: C. 15 V

Applying Kirchhoff's current law at node A and setting the currents flowing out through R1 and R2 equal to the incoming current J gives (VA − 12)/4 + VA/12 = 2. Multiplying both sides by 12 gives 3VA − 36 + VA = 24, so VA = 60/4 = 15 V. Checking with the superposition theorem, E alone contributes 12 × 12/(4 + 12) = 9 V and J alone contributes 2 A × 3 Ω (R1 and R2 in parallel) = 6 V, for a total of 15 V. The node voltage is higher than the source voltage E because the current pushed in by J flows through R1 toward E.

  • A. This is the contribution of the current source J alone (with E shorted); the contribution of E is missing.
  • B. This is the voltage-divider result for the voltage source E alone (with J open); the contribution of J is missing.
  • C. Correct. The node equation gives VA = 15 V.
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More Circuit Analysis: AC, Linear Circuits and Transients questions

  1. In the circuit in the figure, E = 12 V, R1 = 4 Ω and J = 2 A. R2 is removed. Which of the following is the Thevenin equivalent circuit (equivalent voltage Vth and equivalent resistance Rth) seen from the two terminals to which R2 was connected (node A and ground)?
  2. In the circuit in the figure, E = 12 V, R1 = 4 Ω, R2 = 12 Ω and J = 2 A. Which of the following correctly gives the magnitude and direction of the current in R1?
  3. In the circuit in the figure, E1 = 14 V, E2 = 7 V, R1 = 2 Ω, R2 = 1 Ω and R3 = 4 Ω. When the circuit is solved by mesh analysis with the mesh currents I1 and I2 in the directions shown in the figure, which of the following is the magnitude of the current in R3?
  4. The circuit in the figure contains a current-controlled voltage source that produces a voltage r·i (r = 3 Ω) proportional to the current i in R1. With E = 10 V and R1 = 2 Ω, which of the following is the Thevenin equivalent resistance Rth seen from terminals a-b?
  5. In a linear circuit with two sources, which of the following cannot be found with the superposition theorem by applying the sources one at a time and adding the results?