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Find the capacitance of the infinite ladder of capacitors shown in Fig between points A and B . |
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Answer» Solution :Let the net capacitance of the given INFINITE ladder of capacitors between POINTS A and B be C . As the ladder is infinite , addition of one more element of two capacitors `(1 mu F and 2 mu F)` across the points A and B does not change the total capacitance C i.e., value of C should remain unchanged . Let us do it as shown in Fig.  Here , CAPACITOR of `2 mu F ` is in series with C , hence their combined capacitance will be `C. = (C XX 2)/(C + 2) = (2C)/(C + 2) mu F ` This combination is in parallel with capacitor of `1 mu F ` , hence , we have `C = C. + 1 = (2C)/( C+2) + 1` or `C (C +2) = 2C + (C + 2) or C^(2)+ 2 C = 3 C + 2 or C^(2) - C - 2 = 0` On solving the quadratic equation we find that `C = +2` or `-1 mu F ` However , capacitance cannot be negative . Hence , net capacitance of infinite ladder of capacitors `C = +2mu F ` |
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