I'm new to electronics and found a very interesting problem and am very eager to solve it.
You need to calculate the total resistance of an infinite circuit attached below. The resistance of each resistor is 1000 Ω.
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4\$\begingroup\$ Yes, an interesting problem but, you need to ask a question and, if that question is "how do you solve it" then, SE has special rules for homework type problems that require the asker (that's you) to show some effort and try and solve it so that anyone reading your question might be able to see where you are going wrong. Answers on demand are off-topic. The answer is 500 ohms btw. \$\endgroup\$– Andy akaCommented Jan 29, 2023 at 21:17
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2 Answers
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Redraw the first part of the schematic:
simulate this circuit – Schematic created using CircuitLab
What do you imagine as being the voltage difference between A and B? What about the current through \$R_6\$? And given your answers, what do you imagine adding more resistors across points A and B would achieve, exactly?
answered Jan 29, 2023 at 21:48
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1\$\begingroup\$ Thank you, I think I understand it now. If the voltage on input is V, then voltages on R2 and R3 are V/2 on each and on R4 and R5 also V/2 on each. Then we have loop R2, R4, R6 and because R2 and R4 cancel out the voltage on R6 is 0 V so putting more resistors between A and B wouldn't do anything. Now we calculate resistance as if circuit was without "more resistors" and R6 and get the resistance of 500 Ω. Your simplified diagram really helped and i hope I got it right now (i'm new to this). \$\endgroup\$ Commented Jan 29, 2023 at 22:29
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You might choose to split the circuit into contiguous blocks if you didn't know the trick to this answer: -
And you might choose to think that the output of the left circuit block connected to another block with the same input impedance. Only then might you notice this: -
answered Jan 29, 2023 at 22:10