alternating current

Examples of alternating current in the following topics:

• Resistors in AC Circuits

  • Direct current (DC) is the flow of electric charge in only one direction.
  • If the source varies periodically, particularly sinusoidally, the circuit is known as an alternating-current circuit.
  • Current in the resistor alternates back and forth without any phase difference, just like the driving voltage.
  • (a) DC voltage and current are constant in time, once the current is established.
  • Apply Ohm's law to determine current and voltage in an AC circuit

• Phase Angle and Power Factor

  • Impedance is an AC (alternating current) analogue to resistance in a DC circuit.
  • Therefore we can say: the currents in the resistor and capacitor are equal and in phase.
  • (We will represent instantaneous current as i(t). )
  • we notice that voltage $v(t)$ and current $i(t)$ has a phase difference of $\phi$.
  • Because voltage and current are out of phase, power dissipated by the circuit is not equal to: (peak voltage) times (peak current).

• Impedance

  • The phase of the complex impedance is the phase shift by which the current is ahead of the voltage.
  • We use lower case alphabets for voltages and sources to represent that they are alternating (i.e., we use vin(t) instead of Vin(t)).
  • "i" is reserved for alternating currents.
  • Thus the resistor's voltage is a complex, as is the current with an amplitude $I = \frac{V}{R}$.
  • The magnitude of the complex impedance is the ratio of the voltage amplitude to the current amplitude.

• Root Mean Square Values

  • The root mean square (RMS) voltage or current is the time-averaged voltage or current in an AC system.
  • Recall that in the case of alternating current (AC) the flow of electric charge periodically reverses direction.
  • Unlike direct current (DC), where the currents and voltages are constant, AC currents and voltages vary over time.
  • Here, I is the current at time t, and I0=V0/R is the peak current.
  • Relate the root mean square voltage and current in an alternating circut with the peak voltage and current and the average power

• Capacitors in AC Circuits: Capacitive Reactance and Phasor Diagrams

  • The voltage across a capacitor lags the current.
  • When a capacitor is connected to an alternating voltage, the maximum voltage is proportional to the maximum current, but the maximum voltage does not occur at the same time as the maximum current.
  • The value of XC (C standing for capacitor) depends on its capacitance (C) and the frequency (f) of the alternating current.
  • Since the voltage across a capacitor lags the current, the phasor representing the current and voltage would be give as in .
  • The current peaks (has its maximum) one quarter of a wave before the voltage when a capacitor is connected to an alternating voltage.

• Different Types of Currents

  • Direct current (DC) is the unidirectional flow of electric charge.
  • The electric charge flows in a constant direction, distinguishing it from alternating current (AC).
  • A term formerly used for direct current was galvanic current.
  • A direct current circuit is an electrical circuit that consists of any combination of constant voltage sources, constant current sources, and resistors.
  • A particular circuit voltage or current does not depend on the past value of any circuit voltage or current.

• Safety Precautions in the Household

  • A shock hazard occurs when an electric current passes through a person.
  • The two earth/ground connections supply an alternative path through the earth to complete the circuit, since the earth is a good conductor.
  • The alternating current in appliances can induce an EMF on the case.
  • Current that is driven by the induced case EMF is called a leakage current, although current does not necessarily pass from the resistor to the case.
  • It exists at zero volts and supplies an alternative return path for the current through the earth.

• Changing Magnetic Flux Produces an Electric Field

  • In this Atom, we will learn about an alternative mathematical expression of the law.
  • A device that can maintain a potential difference, despite the flow of current is a source of electromotive force.
  • Therefore, we get an alternative form of the Faraday's law of induction: $\nabla \times \vec E = - \frac{\partial \vec B}{\partial t}$.This is also called a differential form of the Faraday's law.
  • Faraday's experiment showing induction between coils of wire: The liquid battery (right) provides a current which flows through the small coil (A), creating a magnetic field.
  • When the coils are stationary, no current is induced.

• Current and Voltage Measurements in Circuits

  • An electrical circuit is a type of network that has a closed loop, which provides a return path for the current.
  • Resistance is inversely proportional to current.
  • More specifically, Ohm's law states that R in this relation is constant, independent of the current.
  • Using this equation, we can calculate the current, voltage, or resistance in a given circuit.
  • Describe the relationship between the electrical current, voltage, and resistance in a circuit

• Energy Stored in a Magnetic Field

  • This changing magnetic flux produces an EMF which then drives a current.
  • When a conductor carries a current, a magnetic field surrounding the conductor is produced.
  • The resulting magnetic flux is proportional to the current.
  • If the current changes, the change in magnetic flux is proportional to the time-rate of change in current by a factor called inductance (L).
  • Thus, inductors oppose change in current by producing a voltage that,in turn, creates a current to oppose the change in magnetic flux; the voltage is proportional to the change in current.