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A network of four 10 muF capacitors is connected to a 500V supply as shown in Fig. Determine the (a) equivalent capacitance of the network and (b) charge on each capacitor. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/PR_XII_V01_C01_S01_379_Q01.png" width="80%">

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Answer Text

Solution :
(a) In fig. `C_(1) , C_(2), C_(3)` are connected in series <br> `:. (1)/(C_(s)) = (1)/(C_(1)) + (1)/(C_(2)) +(1)/(C_(3)) = (3)/(10)` <br> `C_(s) = (10)/(3) muF` <br> This combination is in parallel with `C_(4)` <br> `:.` Equivalent capacitanace, `C = C_(s) + C_(4)` <br> `= (10)/(3) + 10 = 13.3 muF` <br> (b) charge on `C_(1), C_(2). C_(3)` is same = Q say <br> Let charge on `C_(4)` be Q'. <br> `:. (Q)/(C_(1)) + (Q)/(C_(2)) + (Q)/(C_(3)) = 500` <br> `Q((1)/(C_(s))) = 500` <br> or `Q = 500 C_(s) = 500xx(10)/(3) muC = 1.7xx10^(-3) C` <br> Also , `(Q)/(C_(4)) = 500, Q = C_(4)xx500 = 10xx500 mu C` <br> `= 5xx10^(-3)C`

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