Capacitor of 6 microf is conected in parallel with the combination of 4 microf capacitor and a 3 microf capacitor that are in series.Find the net capacitance of the entire combination. Find the...

Capacitor of 6 microf is conected in parallel with the combination of 4 microf capacitor and a 3 microf capacitor that are in series.

Find the net capacitance of the entire combination. Find the potential difference across 3 microf capacitor when 20 V is maintained across the 6 microf capacitor.

Asked on by mabottle

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since the capacitors 3 microF and 4 microF are in series will be replaced by a capacitor that has the capacitance Cs.

1/Cs = 1/4 + 1/3

1/Cs = (3+4)/4*3

1/Cs = 7/12

Cs = 12/7

Now, the capacitor that has the capacitance Cs = 12/7 and the capacitor of 6 microF are in parallel.

The capacitors will be replaced by the capacitor that has the capacitance Cp.

Cp = 12/7 + 6

Cp = (12+7*6)/7

Cp = (12+42)/7

Cp = 54/7 microF

The net capacitance is Cp = 54/7 microF.

Since the capacitor of 6microF and the capacitor of 12/7 microF are in parallel, the potential difference of 20 V across 6 microF is the same across 12/7 microF, too.

Now, we'll determine the charge through 12/7 microF capacitor:

charge = voltage*capacitance

charge = 20V*(12/7) microF

charge = 240/7 microC

The charge on the capacitors of 4 and 3 microF will be the same, since they are in series.

Potential difference across 3 microF capacitor is:

240/7*3 = 240/21 = 80/7 = 11.4 V

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