32.3:
Resistor in an AC Circuit
The alternating current source is a device that supplies a sinusoidally varying voltage or current with time.
A function can describe the sinusoidal voltage or current, where V or I are the voltage or current, respectively, at time t, V0 or I0 are the peak voltage or current, respectively, and ω is the angular frequency.
The sinusoidally varying voltages and currents are represented by rotating vector diagrams.
These vectors rotating counterclockwise at a constant angular frequency are called phasors; the diagrams depicting them are known as phasor diagrams.
Consider a resistor connected across an alternating current voltage source. Recalling Kirchhoff's loop rule, the instantaneous voltage across and the current flowing through the resistor can be determined.
Since the maxima and minima of both curves are reached simultaneously, the curves are said to be in phase.
Therefore, the relationship between current and voltage can be represented using phasor diagrams.
The projections on the vertical axis represent instantaneous voltage and current. Since they are in phase and have the same frequency, their phasors point in the same direction and rotate together.
32.3:
Resistor in an AC Circuit
An alternating emf or voltage source is needed to supply an alternating current (AC) to a circuit. A coil of wire rotating in a magnetic field at a constant angular speed represents such a source. It also generates a sinusoidal alternating emf and serves as an industrial alternator.
One-way current through the meter is measured using diodes. A diode is a device with better conductivity in one direction compared to the other; in its ideal state, it has zero resistance in one direction and allows maximum current to flow, whereas it has high resistance in the other direction to restrict the current. A full-wave rectifier circuit is one possible configuration where, regardless of the direction of the current from the AC source, the current through the galvanometer always flows upward. The average meter deflection is not zero, and it pulses in the same direction at all times.
Rotating vector diagrams are used to depict voltages and currents that vary sinusoidally. The projection of a vector on a horizontal axis with a length equal to the quantity’s amplitude in these diagrams represents the instantaneous value of a quantity that changes sinusoidally with time. At a constant angular speed, the vector rotates counterclockwise. Phasor diagrams are diagrams that include these rotating vectors, also known as phasors. A phasor is not an actual physical quantity, such as a velocity, momentum, or electric field, with a direction in space. Instead, it is a geometrical concept that enables us to describe and examine physical quantities that change sinusoidally over time.
The direction of the current passing through a resistor in an AC circuit has no effect on the resistor's behavior and varies along with the voltage. The peaks of the voltage and current sinosudal waveforms are reached simultaneously at the same instant. Thus, at any point along the horizontal axis, the instantaneous voltage and current are in phase, and their phase angle is zero. Since all of the voltages in purely resistive series AC circuits are in phase with one another, it is possible to add up all of the voltage drops across the resistors to determine the circuit’s overall voltage. Similarly, in a purely resistive parallel AC circuit, all of the individual branch currents can be added to determine the total circuit current because every branch current is in phase with every other branch current.
Suggested Reading
- OpenStax. (2019). University Physics Vol. 2. [Web version], Pg 396 – 398. Retrieved from https://openstax.org/books/university-physics-volume-2/pages/15-2-simple-ac-circuits