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Find the value of \(V_{TH}\) using the Thevenin's theorem of the following circuit :

A 10 V source in series with a 2 ohm resistor feeds a 12 ohm resistor. A 24 ohm resistor is connected across the 12 ohm resistor, and terminals A (top) and B (bottom) lie on the wires joining the 12 ohm and 24 ohm resistors

  • A.7.92 V
  • B.8.57 V
  • C.1.71 V
  • D.8.35 V

Answer: B

The key gives \(V_{TH}\) = 8.57 V.

The key takes the 24 Ω resistor as the load across A-B and removes it. The open-circuit voltage at A-B is then the voltage across the 12 Ω resistor, which forms a divider with the 2 Ω series resistor:

\[ \begin{aligned} V_{TH} &= 10 \times \frac{12}{2 + 12} \\ &= \frac{120}{14} \approx 8.57\ \text{V} \end{aligned} \]

If the 24 Ω resistor were left in place, the parallel combination (8 Ω) would give 8 V, which is not an option, so the question must be read with the 24 Ω resistor as the load. None of 7.92 V, 1.71 V or 8.35 V is the open-circuit voltage of this divider.

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