Capacitive Reactance
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CAPACITVE AND INDUCTIVE REACTANCE The ratio of capacitor voltage to current is called capacitive reactance. and is the opposition in ohms provided by the capacitor. The reactance is inversely proportional to both the frequency and the capacitance. For DC the capacitor is an open. It blocks DC and passes AC. Inductive reactance is determined by both frequency and inductance. The reactance is directly proportional to these terms. Because of inductive reactance a coil has a greater opposition to alternating current than it does to direct current. AC AND THE CAPACITOR In a purely capacitive circuit there is a 90 degree phase relationship between voltage and current. The current begins at the maximum while the voltage begins at zero. When the voltage reaches the maximum the current is zero. Current is always 90 degrees ahead of voltage. The capacitor seems to pass and alternating current. Since current flows easily for a capacitor that is near the discharged state increasing the capacitance reduces the opposition to current flow. Increasing the frequency also decreases the opposition offered by a capacitor. Reactance is different from resistance because reactance is an opposition that is manifested only be alternating current. Resistance is an equal opposition to current flow whether AC or DC. CAPACITIVE REACTANCE (X_{C}) Calculating Capacitance from XC C = 1 / ( 2 pi f X_{C} ) Calculating Frequency from XC f = 1 / ( 2 pi C X_{C} ) SERIES OR PARALLELCONNECTED X_{C} Because capacitive reactance is an opposition expressed in ohms, series or parallel connected reactances are combined the same was as resistanced. SeriesConnected XC X_{CT} = X_{C1} + X_{C2} + ... + X_{CN} ParallelConnected XC X_{CEQ} = 1 / ( 1 / X_{C1} + 1 / X_{C2} + ... + 1 / X_{CN} ) The reciprocal formula is used just as with resistances. AC AND THE INDUCTOR An AC circuit with pure resistance has the alternating current through it and voltage across it rising and falling together. The Inductor's 90 Phase Shift A circuit with pure inductance has a 90 degree phase difference between voltage and current. Because inductance opposes changes in current flow no current flows during the first quarter cycle. Current begins to flow when voltage reaches the maximum. When current reaches the maximum the voltage is back to zero. ELI the ICEman Capacitors and inductors act as opposites. The memory aid ELI the ICEman is helpful. Voltage leads current in an inductive (L) circuit. Current leads voltage in a capacitive (C) circuit. INDUCTIVE REACTANCE (X_{L}) The greater the inductance the greater the opposition to AC. Also greater frequency the greater the opposition. Inductive reactance is measured in ohms and its symbol is XL. Calculating Inductance from X_{L} L = X_{L} / 2 pi f Calculating Frequency from X_{L} f = X_{L} / 2 pi L SERIES OR PARALLELCONNECTED X_{L} SeriesConnected X_{L} X_{LT} = X_{L1} + X_{L2} + ... + X_{LN} Inductive reactances are summed just as with resistances. Parallel Connected X_{L} X_{LEQ} = 1 / ( 1 / X_{L1} + 1 / X_{L2} + ... + 1 / X_{LN} ) Parallel reactances are combined using the reciprocal formula just as with resistance. THE QUALITY FACTOR, Q The quality factor of a coil is and indication of the coils ability to store energy (and later release it) rather than dissipate it as heat. Q = X_{L} / R_{i} Effective Resistance At low frequencies the Ri is just the DC resistance of the conductor in the coil. At higher frequencies losses due to eddy currents, hysteresis, and other losses become apparent. This is known as AC resistance to differentiate it from DC conductor losses. Q = X_{L} / R_{e} Reducing Effective Resistance Air cores are used for high frequency coils. Stranded wire with insulated strands may be used to reduce skin effect. 