Question

In the circuit given below, it is given that VAB = 4 V for RL = 10 kΩ and VAB = 1 V for RL = 2kΩ. The values of the Thevenin resistance and voltage for the network N are ____________

(a) 16 kΩ and 30 V

(b) 30 kΩ and 16 V

(c) 3 kΩ and 6 V

(d) 50 kΩ and 30 V

The question was posed to me in a national level competition.

The origin of the question is Thevenin Theorem Involving Dependent and Independent Sources in portion Useful Theorems in Circuit Analysis of Network Theory

Answer 1

Right choice is (b) 30 kΩ and 16 V

To elaborate: When RL = 10 kΩ and VAB = 4 V

Current in the circuit I = \(\frac{V_{AB}}{R_L} = \frac{4}{10}\) = 0.4 mA

Thevenin voltage is given by VTH = I (RTH + RL)

= 0.4(RTH + 10)

= 0.4RTH + 4

Similarly, for RL = 2 kΩ and VAB = 1 V

So, I = \(\frac{1}{2}\) = 0.5 mA

VTH = 0.5(RTH + 2)

= 0.5 RTH + 1

∴ 0.1RTH = 3

Or, RTH = 30 kΩ

And VTH = 12 + 4 = 16 V.