XC = -1 / (2 pi f C)
XC = about -2653 ohms
The minus sign indicates the current is leading in the this case. Treat it as if the sign were not there.
Do it yourself, the equation is: XC = 1/( 2 pi f C)
In the basic configuration, a capacitor is constructed with two parallel conductor plates with a layer of insulating material in between. When the cap is hooked up to the AC power supply, the voltage (v) across the plates and the charge (q) induced on the plates follow this capacitance expression: C = dq/dv or i = C dv/dt, where C is determined by the properties of the insulating material and the geometry of the cap (in the case of the parallel plates, the separation between the two electrodes (t). For the parallel plates, C can be written as (dielectric constant * plate area / t). Electrically, the change in the charge induced on the plates (dq), is directly related to the change in voltage difference (dv) between the two plates, since C is a constant. Theoretically, no energy is lost by charging and discharging the cap with an AC current. When the cap absorbs electrical energy from the power supply, it stores the energy in the electric field in the insulator. When discharging, the cap gives the stored energy back to the circuit -- hence, no energy loss. In a circuit, we use the cap to prolong/smoothen/resist any voltage change in time or to absorb a sudden energy surge (electrostatic discharge and power-line glitches, for example).
It is 100+j(500-300) ohm = (100+j200) ohm = 223.6<630 ohm
1/(2 Pi sqrt(LC))
100 WVDC means 100 working volts DC. That is the maximum operating voltage that the capacitor is certified to have across it. Exceeding that rating could puncture a hole in the dielectric, leading to catastrophic failure of the capacitor.
To determine the required capacitance for a 6 volt 100 amp rectifier, you would need to know the ripple voltage that the circuit would tolerate. You would also need to know the ripple frequency. More specifically, you would need to know the time from one peak value to the intersection of the capacitor's voltage decay curve and the next turn on point for the rectifier.Let's say that the tolerated ripple voltage is 1 volt, and that the ripple frequency is 120 hertz, as provided by a full wave rectifier. This is a period of 8.3 millseconds. The actual time from ripple peak to ripple trough is actually slightly less than 8.3 millseconds, but that is a function of ripple slope, as somewhat complex calculation, so lets use 8.3 millseconds, which will be conservative.1 volt in 8.3 millseconds is 120 volts per second. Plug that in to the equation for a capacitor ...dv/dt = i/c..., along with the current of 100 ampere, solve for c and you get ...dv/dt = i/c120 = 100/cc = 100/120c = 0.83 faradsNow, 8.3 farads is a very large capacitor. Lets improve the situation with a three phase rectifier. In that case, the ripple frequency is 360 hertz, or 2.8 milliseconds, requiring a 0.28 farad capacitor, still a large value, but better than 0.83 farads.
The reactance of a capacitor depends on its capacitanceand the frequency of the voltage across it.In general, the magnitude of capacitive reactance is . . .1 / (2pi x frequency x capacitance)At 100 Hz, that would be0.00159 / (capacitance) in Farads .
If current and voltage of an AC are in phase, then the "power factor" is 100%, and the load is a pure resistance, with no inductive or capacitive reactance (at least at the operating frequency of the AC).
In the basic configuration, a capacitor is constructed with two parallel conductor plates with a layer of insulating material in between. When the cap is hooked up to the AC power supply, the voltage (v) across the plates and the charge (q) induced on the plates follow this capacitance expression: C = dq/dv or i = C dv/dt, where C is determined by the properties of the insulating material and the geometry of the cap (in the case of the parallel plates, the separation between the two electrodes (t). For the parallel plates, C can be written as (dielectric constant * plate area / t). Electrically, the change in the charge induced on the plates (dq), is directly related to the change in voltage difference (dv) between the two plates, since C is a constant. Theoretically, no energy is lost by charging and discharging the cap with an AC current. When the cap absorbs electrical energy from the power supply, it stores the energy in the electric field in the insulator. When discharging, the cap gives the stored energy back to the circuit -- hence, no energy loss. In a circuit, we use the cap to prolong/smoothen/resist any voltage change in time or to absorb a sudden energy surge (electrostatic discharge and power-line glitches, for example).
It is 100+j(500-300) ohm = (100+j200) ohm = 223.6<630 ohm
Impedance (Z) = Resistance (R) + Reactance (X)Resistance is real. Reactance is imaginary.Z = R + jXAn ideal capacitor has only reactance.Z = 0 + jXReactance of a capacitor is given by X = 1/(jwC).Where:Angular frequency (w) = 2*pi*frequencyCapacitance (C) = 12 microfarads (uF) in our caseZ = 1/( j*2*pi*100 Hz*10^-6 uF ) = 13.26/j uF = j13.26/( j*j ) uF = -j13.26 uF
No, as 100% efficiency is not possible.AnswerYes, it occurs at resonance. That is, when a circuit's inductive reactance is exactly equal to its capacitive reactance. This can be achieved by adjusting the frequency of the supply until resonance is achieved. Incidentally, power factor has nothing to do with 'efficiency'.
The reactance of an inductor is calculated as Xl = 2πfL, where Xl is the inductive reactance, f is the frequency, and L is the inductance. Substituting the given values of 100 microhenries for inductance and 400 Hz for frequency into the formula gives Xl = 2 * π * 400 * 100 * 10^-6 which equals approximately 251.3 ohms.
You want a power factor of 1 or 100%, which is a purely resistive circuit. If you have a motor or some other inductive load in a circuit the total voltage and total current in the circuit will not be in phase (phase shift), your power factor will be less than 1. By adding a capacitor (180 degrees out of phase with inductive load) to the circuit that has a capacitive reactance equal to the inductive reactance of the motor, you can cancel the phase shift and have an ideal power factor (no wasted power). Anything above .9 would be good.
1/(2 Pi sqrt(LC))
The run capacitor has to absorb the VARs while the motor is running, but the start capacitor has to provide running current to start the motor. The latter is higher, so more microfarads are needed to pass the greater current. Current in a capacitor is 2pi x frequency x capacitance x voltage so, on a 240 v 50 Hz system, 100 mfd would take 2pi x 50 x 100 x 10-6 x 240 amps, and that is multiplied by the voltage 240 to find the VARs.
100 WVDC means 100 working volts DC. That is the maximum operating voltage that the capacitor is certified to have across it. Exceeding that rating could puncture a hole in the dielectric, leading to catastrophic failure of the capacitor.
1------------10000001 100