A 30-uf capacitor is charged to 80 V and then connected across aninitially uncha

Question

A 30-uf capacitor is charged to 80 V and then connected across aninitially uncharged capacitor of unknown capacitance C. If thefinal potential difference across the 30-uf capacitor is 20 V,determine C.
The answer is 90 uf but how do you get that answer?
The answer is 90 uf but how do you get that answer?

Explanation / Answer

If the final potential difference across the 30 uF capacitoris 20 V, then the final potential difference between the plates ofC will also be 20V. We know that                         Q = CV So that the charge that went into the initially unchargedcapacitor is            Qinitial - Q final = C (Vinitial -Vfinal) ==>   Q = (30F)(80V - 20V) =(30F)(60V) This charge that was lost by the first capacitor will be thecharge gained by the second capacitor. so Q = CV We know that the final voltage is 20 V    Now solve for C. C =Q/V     = (30F)(60V)/(20V)                     = 90F

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