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Vanessa23
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[SOLVED] Infinite capacitors
Consider the infinite chain of capacitor problem:
Each of the capacitors (C) below in the infinite series circuit has a capacitance of 6.34 mF. What is the capacitance of a single capacitor that can be connected between points A and B to replace the “chain”? (The picture of the capacitor should be attached to this thread)
Then the real question:
suppose that each of the capacitors in the chain has a capacitance of 21-mfarads. What is the equivalent capacitance of the infinite chain?
a hint: 5 = [x + {x + (x + . . . )1/2}1/2]1/2
Solve for x: x = 20
Q=CV and CT=C1+C2+C3 for parallel chains but capacitors in series
add as 1/CT=1/C1 + 1/C2 + 1/C3
For the first part, it would have to be equal to 3 parallel capacitors in series with 4 capacitors, which I assume is where the hint comes from.
I am assuming that the x=20 means that there are 20 xs in the equation? and that you solve for x, but then why do you never take into consideration the 6.34mF?
or is the hint for the second part of the problem?
Homework Statement
Consider the infinite chain of capacitor problem:
Each of the capacitors (C) below in the infinite series circuit has a capacitance of 6.34 mF. What is the capacitance of a single capacitor that can be connected between points A and B to replace the “chain”? (The picture of the capacitor should be attached to this thread)
Then the real question:
suppose that each of the capacitors in the chain has a capacitance of 21-mfarads. What is the equivalent capacitance of the infinite chain?
Homework Equations
a hint: 5 = [x + {x + (x + . . . )1/2}1/2]1/2
Solve for x: x = 20
Q=CV and CT=C1+C2+C3 for parallel chains but capacitors in series
add as 1/CT=1/C1 + 1/C2 + 1/C3
The Attempt at a Solution
For the first part, it would have to be equal to 3 parallel capacitors in series with 4 capacitors, which I assume is where the hint comes from.
I am assuming that the x=20 means that there are 20 xs in the equation? and that you solve for x, but then why do you never take into consideration the 6.34mF?
or is the hint for the second part of the problem?