AC
(noun)
Alternating current.
Examples of AC in the following topics:
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Complement of an event
- (b) Compute P(Ac) and P(Bc).
- The complement of event A is denoted Ac, and Ac represents all outcomes not in A.
- A and Ac are mathematically related: P(A) + P(Ac) = 1, i.e.
- P(A) = 1 - P(Ac) (2.25)
- (b) P(Ac) = 1/36.
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Resistors in AC Circuits
- Ohm's law applies to AC circuits as well as to DC circuits.
- Therefore, with an AC voltage given by:
- (b) A graph of voltage and current versus time for 60-Hz AC power.
- The frequencies and peak voltages of AC sources differ greatly.
- Apply Ohm's law to determine current and voltage in an AC circuit
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Inductors in AC Circuits: Inductive Reactive and Phasor Diagrams
- In an AC circuit with an inductor, the voltage across an inductor "leads" the current because of the Lenz' law.
- Suppose an inductor is connected directly to an AC voltage source, as shown in .
- This is considered an effective resistance of the inductor to AC.
- (a) An AC voltage source in series with an inductor having negligible resistance.
- Explain why the voltage across an inductor "leads" the current in an AC circuit with an inductor
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Root Mean Square Values
- Recall that most residential and commercial power sources use AC.
- For example, Ohm's Law for AC is written as follows:
- AC power as a function of time.
- (b) A graph of voltage and current versus time for 60-Hz AC power.
- The frequencies and peak voltages of AC sources differ greatly.
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Hypergeometric Distribution
- Given this sampling procedure, what is the probability that exactly two of the sampled cards will be aces (4 of the 52 cards in the deck are aces).
- In this example, k = 4 because there are four aces in the deck, x = 2 because the problem asks about the probability of getting two aces, N = 52 because there are 52 cards in a deck, and n = 3 because 3 cards were sampled.
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Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams
- In the previous Atom on "Resistors in AC Circuits", we introduced an AC power source and studied how resistors behave in AC circuits.
- There, we used the Ohm's law (V=IR) to derive the relationship between voltage and current in AC circuits.
- If the AC supply is connected to a resistor, then the current and voltage will be proportional to each other.
- Since an AC voltage is applied, there is an rms current, but it is limited by the capacitor.
- This is considered to be an effective resistance of the capacitor to AC, and so the rms current Irms in the circuit containing only a capacitor C is given by another version of Ohm's law to be $I_{rms} = \frac{V_{rms}}{X_C}$, where Vrms is the rms voltage.
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Transitivity
- A strong transitivity is one in which there are connections AB, BC, and AC, and the connection AC is stronger than the Min value of Strong tie.
- A weak transitivity is one in which there are connections AB, BC and AC, and AC; the value of AC is less than the threshold for a strong tie, but greater than the threshold Min value of Weak tie.
- A Euclidean transitivity is defined as a case where AB, BC, and AC are present, and AC has a value less than the sum of AB + BC.
- A Stochastic transitivity is defined as the case where AB, BC, and AC are present, and AC is less than the produce AB*BC.
- That is, there are 146 cases where, if AB and BC are present, then AC is also present.
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Addition, Subtraction, and Multiplication
- $(a + bi)(c + di) = (ac - bd) + (bc + ad)i$
- $(a + bi)(c + di) = ac + bci + adi + bidi$ (by the distributive law)
- = $ac + bidi + bci + adi$ (by the commutative law of addition)
- = $ac + bdi^2 + (bc + ad)i$ (by the commutative law of multiplication)
- = $(ac - bd) + (bc + ad)i$ (by the fundamental property of the imaginary unit)
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Phase Angle and Power Factor
- In a series RC circuit connected to an AC voltage source, voltage and current maintain a phase difference.
- Impedance is an AC (alternating current) analogue to resistance in a DC circuit.
- In a series RC circuit connected to an AC voltage source as shown in , conservation of charge requires current be the same in each part of the circuit at all times.
- where $\omega$ is the angular frequency of the AC voltage source and j is the imaginary unit; j2=-1.
- Compare the currents in the resistor and capacitor in a series RC circuit connected to an AC voltage source
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The Inventions of the Telephone and Electricity
- When George Westinghouse suggested using high-voltage AC instead, as it could carry electricity hundreds of miles with only marginal loss of power, Edison waged a "War of Currents" to prevent the adoption of the AC system.
- The war against AC involved Edison in the development and promotion of the electric chair (using AC) as an attempt to portray AC as having greater lethal potential than DC.
- Edison continued to carry out a brief but intense campaign to ban the use of AC or to limit the allowable voltage for safety purposes.
- As part of this campaign, Edison's employees publicly electrocuted animals to demonstrate the dangers of AC.
- AC eventually replaced DC in most instances of generation and power distribution, enormously extending the range and improving the efficiency of power distribution.