BASICS OF ELECTRICITY - 5
CALCULATING THE TIME CONSTANT OF A CAPACITIVE CIRCUIT:
Time constant is decided by the symbol "T".To determine the time constant of a capacitive circuit, use oneof the following formulas:
T(in seconds) = R(megohms) X C(microfarads)
T(in microseconds) = R(megohms) X C(pico farads)
T(in microseconds) = R(ohms) X C (microfarads)
In the following illustration, C1 is equal to 2 mF, and R1 is equalto 10 W. When the switch is closed, it will take20microseconds for voltage across the capacitor to risefrom zero to 63.2% of its maximum value. There are fivetime constants, so it will take 100 microseconds for this voltageto rise to its maximum value.
FORMULA FOR SERIES CAPACITORS:
Connecting capacitors in series decreases total capacitance.The effect is like increasing the space between the plates. Therules for parallel resistance apply to series capacitance. In thefollowing circuit, an AC generator supplies electrical power tothree capacitors. Total capacitance is calculated using thefollowing formula:
1/Ct = 1/C1+1/C2+1/C3
1/Ct = 1/5+1/10+1/20 = 7/20 = 2.86
FORMULA FOR PARALLES CAPACITORS:
In the following circuit, an AC generator is used to supplyelectrical power to three capacitors. Total capacitance is calculatedusing the following formula:
Ct = C1+C2+C3
INDUCTIVE AND CAPACITANCE REACTANCE:
In a purely resistive AC circuit, opposition to current flow is called resistance. In an AC circuit containing only inductance,capacitance, or both, opposition to current flow is called reactance. Total opposition to current flow in an AC circuit that contains both reactance and resistance is called impedance designated by the symbol Z. Reactance and impedance are expressed in ohms.
Inductance only affects current flow when the current is changing. Inductance produces a self-induced voltage(counter emf) that opposes changes in current. In an ACcircuit, current is changing constantly. Inductance in an AC circuit, therefore, causes a continual opposition. This opposition to current flow is called inductive reactance, and is designated by the symbol XL. Inductive reactance is dependent on the amount of inductance and frequency. If frequency is low current has more time to reach a higher value before the polarity of the sine wave reverses. If frequency is high current has less time to reach a higher value. In the following illustration, voltage remains constant. Current rises to a higher value at a lower frequency than a higher frequency.
In a 60 hertz, 10 volt circuit containing a 10 mh inductor, the inductive reactance would be:
Xl = 2 x 3.14 x 60 x .010 = 3.768 ohms
Once inductive reactance is known, Ohmís Law can be usedto calculate reactive current.
I = E/Z = 10/3.768 = 2.65 amps
PHASE RELATIONSHIP BETWEEN CURRENT AND VOLTAGE IN AN INDUCTIVE CIRCUIT:
Current does not rise at the same time as the source voltage in an inductive circuit. Current is delayed depending on the mount of inductance. In a purely resistive circuit, current and voltage rise and fall at the same time. They are said to be ìinphase.î In this circuit there is no inductance, resistance andimpedance are the same.
In a purely inductive circuit, current lags behind voltage by 90 degrees. Current and voltage are said to be "out of phase". In this circuit, impedance and inductive reactance are the same.
All inductive circuits have some amount of resistance. AC current will lag somewhere between a purely resistive circuit,and a purely inductive circuit. The exact amount of lag depends on the ratio of resistance and inductive reactance. The more resistive a circuit is, the closer it is to being in phase.The more inductive a circuit is, the more out of phase it is. In the following illustration, resistance and inductive reactance are equal. Current lags voltage by 45 degrees.
When working with a circuit containing elements of inductance,capacitance, and resistance, impedance must becalculated. Because electrical concepts deal with trigonometric functions, this is not a simple matter of subtraction and addition. The following formula is used to calculate impedance in an inductive circuit:
In the circuit illustrated above, resistance and inductive reactance are each 10 ohms. Impedance is 14.1421 ohms. A simple application of Ohmís Law can be used to find total circuit current.
Another way to represent this is with a vector. A vector is a graphic representation of a quantity that has direction and 50 miles southwest from another. The magnitude is 50 miles,and the direction is southwest. Vectors are also used to show electrical relationships. As mentioned earlier, impedance (Z) is the total oppositon to current flow in an AC circuit containing resistance, inductance, and capacitance. The following vector illustrates the relationship between resistance and inductive reactance of a circuit containing equal values of each. The angle between the vectors is the phase angle represented by the symbol q. When inductive reactance is equal to resistance the resultant angle is 45 degrees. It is this angle that determines how much current will lag voltage.
Capacitance also opposes AC current flow. Capacitive reactance is designated by the symbol XC. The larger the capacitor,the smaller the capacitive reactance. Current flow in a capacitive AC circuit is also dependent on frequency. Thefollowing formula is used to calculate capacitive reactance:
Xc = 1/2 x 3.14 x f x C
Capacitive reactance is equal to 1 divided by 2 times pi, times the frequency, times the capacitance. In a 60 hertz, 10 volt circuit containing a 10 microfarad capacitor the capacitivereactance would be:
Xc = 1/2 x 3.14 x f x C = 1/(2 x 3.14 x 60 x 0.000010) = 265.39 ohms
Once capacitive reactance is known, Ohmís Law can be used to calculate reactive current.
I = E/Z = 10/ 265.39 = 0.0376 amps
PHASE RELATIONSHIP BETWEEN CURRENT AND VOLTAGE IN AN CAPACITIVE CIRCUIT:
The phase relationship between current and voltage are opposite to the phase relationship of an inductive circuit. In a purely capacitive circuit, current leads voltage by 90 degrees.All capacitive circuits have some amount of resistance. AC current will lead somewhere between a purely resistive circuit and a purely capacitive circuit. The exact amount of lead depends on the ratio of resistance and capacitive reactance.The more resistive a circuit is, the closer it is to being in phase. The more capacitive a circuit is, the more out of phase it is. In the following illustration, resistance and capacitive reactance are equal. Current leads voltage by45 degrees.
CALCULATING IMPEDENCE IN A CAPACITIVE CIRCUIT:
The following formula is used to calculate impedence in a capacitive circuit
In the cirucuit illustrated above, resistance and capacitivef reactance are each 10 ohms. Impedence is 14.1421 ohms.
The following vector illustrates the relationship betweenresistance and capacitive reactance of a circuit containingequal values of each. The angle between the vectors is thephase angle represented by the symbol q. When capacitivereactance is equal to resistance the resultant angle is -45degrees. It is this angle that determines how much currentwill lead voltage.
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