5. Error Analysis. Suppose that the capacitor used in this lab is replaced by a

Question

5. Error Analysis. Suppose that the capacitor used in this lab is replaced by a series combination of two capacitors. C1 and C2. The net capacitance of the capacitor for our experiment is then expressed as (1/C) = (1/C1) + (1/C2). The values of C1 and C2 are known within the uncertainties, Delta C1 and Delta C2, respectively (C1 = C1 plus minus Delta C1, and C2 = C2 plus minus Delta C2) Using the general formula for error propagation, express the uncertainty (Delta C) in the value of C in terms of Delta C1 and Delta C2. [A similar problem for a certain resistor-combination is given as an worked out example in the Appendix section of this lab manual].

Explanation / Answer

By derivatives,

1/C^2 dC = 1/C1^2 dC1 + 1/C2^2 dC2

Thus,

dC = C^2[dC1/C1^2 + dC2/C2^2]   [ANSWER]

where C = C1C2/(C1 + C2).

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