You have designed a system that uses a 200mirofarad capacitorwhich is cylindrica

Question

You have designed a system that uses a 200mirofarad capacitorwhich is cylindrical in shape with a diameter of .001 meters and alength of .03 meters. The capacior has am AC rating of300 Volts.  A 50% saftey factor is required at alltimes. An AC voltage of 120 volts would be applied to thecapacitor, but the length of the capacitor is to long for the boxthat the electrical system goes in. The manufacturer of thecapacior suggests keeping the capacitance down by reducing theapplied AC potential. You manage to get the applied ACVolage down to 90 Volts. Keeping the original diameter, whatnew capacitor lenght should you expect using the same capacitiormanufactuing technology and safty facor? Any Help would be great? You have designed a system that uses a 200mirofarad capacitorwhich is cylindrical in shape with a diameter of .001 meters and alength of .03 meters. The capacior has am AC rating of300 Volts.  A 50% saftey factor is required at alltimes. An AC voltage of 120 volts would be applied to thecapacitor, but the length of the capacitor is to long for the boxthat the electrical system goes in. The manufacturer of thecapacior suggests keeping the capacitance down by reducing theapplied AC potential. You manage to get the applied ACVolage down to 90 Volts. Keeping the original diameter, whatnew capacitor lenght should you expect using the same capacitiormanufactuing technology and safty facor? Any Help would be great?

Explanation / Answer

the charge on the capacitor is Q = C * V C = 200 microfarad = 200 F = 200 * 10-6F V = 300 Volts Q = 200 * 10-6 * 300 = 6 * 10-2 C the charge on the capacitors is same when the AC voltage is120 V and the AC voltage is 90 V therefore we get Q = C1 * V1 -----------(1) and Q = C2 * V2 ------------(2) where C = (2koL/ln(b/a)) the diameter of the capacitor is same,therefore,the termln(b/a) is constant (2)/(1) (Q/Q) = (C1 * V1 /C2 *V2) or 1 = (C1 * V1 /C2 *V2) or C1 * V1 = C2 *V2 or (C1/C2) =(V2/V1) V2 = 90 V and V1 = 120 V or (C1/C2) = (90/120) = 0.75 or C1 = 0.75 * C2 or [(2ko * L1)/ln(b/a)] =0.75 * [(2ko * L2)/ln(b/a)] or L1 = 0.75 * L2 or L2 = (L1/0.75) = (.03/0.75) = 0.04m or L2 = (L1/0.75) = (.03/0.75) = 0.04m

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