English
Menu

Circuit Analysis: AC, Linear Circuits and Transients

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?

Circuit with a current-controlled voltage source + E R1 i + − r·i a b Rth?
Circuit with a current-controlled voltage source · View in diagrams
  1. A−1 Ω
  2. B2 Ω
  3. C5 Ω
Show answer and explanation

Answer: C. 5 Ω

The voltage at terminal a is E minus the voltages across R1 and the dependent source: Va = 10 − 2i − 3i = 10 − 5i. With the terminals open, i = 0, so the open-circuit voltage is 10 V; with them shorted, 10 − 5i = 0 gives a current of 2 A, so Rth = 10/2 = 5 Ω. Setting E to 0 and applying a voltage V to the terminals gives V = −5i, so V/(−i) = 5 Ω as well. A dependent source takes its value from a current in the circuit, so it must not be set to 0 the way an independent source is.

  • A. This is 2 − 3 = −1 Ω, taking the dependent source in the opposite direction (aiding E). In the figure, i enters the + side, so the source acts as a voltage drop.
  • B. This sets the dependent source to 0 (shorted) like an independent source and sees only R1.
  • C. Correct. Voc/Isc = 10 V/2 A = 5 Ω.
Practice this topic Back to topic

Books on Circuit Analysis: AC, Linear Circuits and Transients Ad

As an Amazon Associate I earn from qualifying purchases.

More Circuit Analysis: AC, Linear Circuits and Transients questions

  1. 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?
  2. In a linear resistive circuit whose only sources are two DC voltage sources E1 and E2, the voltage Vo across a resistor is measured. With E1 = 1 V and E2 = 0 V, Vo = 2 V; with E1 = 0 V and E2 = 1 V, Vo = −1 V. Which of the following is Vo when E1 = 3 V and E2 = 2 V?
  3. Treating the T network in the figure as a two-port with R1 = 2 Ω, R2 = 3 Ω and R3 = 6 Ω, which of the following is the correct set of Z parameters (V1 = z11 I1 + z12 I2, V2 = z21 I1 + z22 I2)?
  4. In the RC circuit in the figure, a DC voltage E is applied to an uncharged capacitor by closing the switch at t = 0. With the time constant τ = RC, which of the following is closest to the capacitor voltage vC at t = 5τ, as a percentage of the final value E?
  5. In the RC circuit in the figure, E = 10 V, R = 10 kΩ and C = 100 µF, and the capacitor is initially uncharged. Which of the following is closest to the capacitor voltage vC 2 seconds after the switch is closed at t = 0?