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What is series connection of capacitors ? |
Answer» Solution :Figure shows CAPACITORS `C_(1)` and `C_(2)` combined in series. The left plate of `C_(1)` and the right plate of `C_(2)` are connected to two terminals of a battery and have charges Q and -Q. HENCE, the right plate of `C_(1)` has charge - Q and the left plate of `C_(2)` induces charge + Q. Hence, both capacitors have same charge on each capacitor even though they have different capacitance. Suppose, potential difference between two PLATES of capacitor `C_(1)` and `C_(2)` are `V_(1)` and `V_(2)` respectively. If potential difference between two ends of combination V, then `V=_(1)+V_(2)` `:. V= (Q)/(C_(1))+(Q)/(C_(2)) [ because C=(Q)/(V) implies V = (Q)/(C)]` `:. (V)/(Q)=(1)/(C_(1))+(1)/(C_(2))` This combination as an effective capacitor with charge Q and potential difference V. The effective capacitance of the combination is, `C=(Q)/(V)` `:.` From equation (2) and (3) `(1)/(C) =(1)/(C_(1))+(1)/(C_(2))` |
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