Trouble getting the provided answer in a Thevenin problem

cranberrysky

Joined Feb 15, 2022
54
From question 8 of the Thevenin’s, Norton’s, and Maximum Power Transfer Theorems Worksheet:

Thévenize this resistive network:
The answer says the voltage is 8.772 V and the resistance is 210.53 Ohms:
I got the right value for voltage. I can't figure out where the resistance comes from.

For resistance, I calculated the total resistance with 300 and 1k in parallel, that resistance in series with 400, and that resistance in parallel with 2k. And what I get is:
$\frac{(\frac{1000*300}{1000+300}+400)*2000}{(\frac{1000*300}{1000+300}+400)+2000}\approx479.532$

I even simulated the circuit on an app to see if I made a math mistake, and that's the resistance I get between the two rightmost nodes. I'm inclined to think it's a mistake in the worksheet, but maybe I just don't understand Thevenin's Theorem.

Jony130

Joined Feb 17, 2009
5,475
It looks like your calculation is correct. Let me check it Rth = Vth/Isc, And the Isc will be Isc = 15V/(1kΩ||0.4kΩ + 0.3kΩ) * 1k/1.4kΩ ≈ 18.3mA . So the Rth = 8.772V/18.3mA ≈ 479Ω

Irving

Joined Jan 30, 2016
3,548
Yes, there is an error in the worksheet. The 210.53 ohms is 300 || 1k || 2.4k but they've forgotten that the output isn't across the 1k || 2.4k but across the 2k portion of the 2.4k...

The correct value is (300 || 1k + 400) || 2k = (230.79 + 400) || 2k = 630.79 || 2k = 479.53 ohm

cranberrysky

Joined Feb 15, 2022
54
Ok, thanks to both of you.