Infinite grid
×××
Find the effective capacitance between two adjacent points if each capacitor is of same value( ) .
If
Find .
The answer is 3.
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1 solution
Guessed work but my first guess was treated as correct. Because of Level 2 stated.
C~C // C // C~C = 2 C {5 capacitors connected.}
1.5 C~1.5 C // C // 1.5 C~1.5 C = 2.5 C {13 capacitors connected.}
But we know that the capacitance is certainly greater than 2.5 C of only few partial connections.
2 C~2 C // C // 2 C~2 C = 3 C {To a limit by imagination when 1.5 C can become 2 C.}
I was ready to guess for 3 and then 4. If 3 and 4 are not the answer, then I may guess for values between 3 and 4. I need to simulate actually to know the exact answer for certain but I haven't got to do this.
To isolate top and bottom for ease of only in parallel or in series, an X-shape consists of 21 capacitors are constructed as:
1.6 C~1.6 C // C // 1.6 C~1.6 C = 2.6 C {Quite populated up to this stage as can be seen from diagram.}
Capacitor on left and on right of terminals measured are not in complete connections. But any capacitor connected via many steps or far outside shall not contribute much capacitance onto the man circuit.
Answer: 3 (Guessed)