4. Determine the capacitance of a single capacitor that will have the same effec

Question

4. Determine the capacitance of a single capacitor that will have the same effect as a combination shown in Fig. 1. The capacitances of the capacitors are as follows: C1 = 100 µF; C2 = 200 µF; C3 = 120 µF; C4 = 180 µF . Find the charges stored in each capacitor and the potential differences between the plates of each capacitor if the voltage V between the points a and b is 100 V.

(a) C1 C2 C3 (b)
*----| |-----| |---*------| |------*
/
----| |----/
C4

How much electric energy can be stored in such a combination of the capacitors?

ANS :

Explanation / Answer

if C1, C2, and C3 are series, in parallel with C4 then Ceq=1/(1/100+1/200+1/120)=42.86E-6F for series part Ceq+C4=42.86+180=222.86E-6F for system system charge: 222.86*100=22286E-6C charge on 180E-6*100= 18000E-6C therefore charge on C1, C2, C3=22286-18000=4286E-6C they all carry the same charge because they are in series (C1, C2, C3) C4 VD=100V C3 VD=4286E-6/120E-6=35.71V C2 VD=4286E-6/200E-6=21.43V C1 VD=4286E-6/100E-6=42.86V

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