Equivalent capacitance!

It's quite interesting!

#Physics #ElectricityAndMagnetism #PhysicsProblem

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Comments

Between which two points are we trying to find the equivalent capacitance?

Jimmy Kariznov - 7 years, 10 months ago

Assuming you mean between the leftmost two points, we have $C_{eq} \approx 1.389260105247235 \cdot C$ .

Now, can anyone find a closed form for this?

Jimmy Kariznov - 7 years, 10 months ago

Can you tell me the process?

Advitiya Brijesh - 7 years, 10 months ago

@Advitiya Brijesh – I wrote a program to calculate $C_{eq}(n)$ for $n = 1, \ldots, 100$ . The convergence was exponential, specifically $C_{eq}(n) \approx (1.38926 - 0.80082 \cdot 0.07714^n)C$ .

While this doesn't solve anything, it might give someone a hint as to how to proceed.

Jimmy Kariznov - 7 years, 10 months ago

Are you sure if there exists closed-form solution?

Pontus Hultkrantz - 7 years, 9 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$