CourseNotes.23

# CourseNotes.23 - considered to be an equivalent capacitor...

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Unformatted text preview: considered to be an equivalent capacitor of C eq 1 = C 1 + C 2 . Now that we have turned these into an equivalent system, we can consider this equivalent capacitor to be in series with C 3 . The equivalent capacitance of the entire circuit is therefore 1 C eq 2 = 1 C 3 + 1 C eq 1 ⇒ C eq 2 = C 3 ( C 1 + C 2 ) C 1 + C 2 + C 3 Our goal now is to find the initial charge and potential on C 1 , but it will be easier to take it is steps. We will thus begin by finding the charge and potential across the equvalent capacitor C eq 1 . The total charge across the entire circuit is q tot = C eq 2 V Since C 3 and C eq 1 are in series, they both must have equal charge across them so q eq 1 = q tot = C eq 2 V . We can use this fact to find the potential across C eq 1 via V eq 1 = q tot C eq 1 = C eq 2 V C eq 1 = C 3 V C 1 + C 2 + C 3 We can now step down one more level to the original circuit. Since C 1 and C 2 are in parallel the potential across each must be the same, so we have found V 1 = V eq 1...
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