parallel equivalent resistance

Examples of parallel equivalent resistance in the following topics:

• Resistance and Resistivity

  • The potential difference (voltage) seen across the network is the sum of those voltages, thus the total resistance (the series equivalent resistance) can be found as the sum of those resistances:
  • Thus the equivalent resistance (Req) of the network can be computed:
  • The parallel equivalent resistance can be represented in equations by two vertical lines "||" (as in geometry) as a simplified notation.
  • For the case of two resistors in parallel, this can be calculated using:
  • As a special case, the resistance of N resistors connected in parallel, each of the same resistance R, is given by R/N.

• Combination Circuits

  • In that case, wire resistance is in series with other resistances that are in parallel.
  • In the figure, the total resistance can be calculated by relating the three resistors to each other as in series or in parallel.
  • For more complicated combination circuits, various parts can be identified as series or parallel, reduced to their equivalents, and then further reduced until a single resistance is left, as shown in .
  • Combination circuit can be transformed into a series circuit, based on an understanding of the equivalent resistance of parallel branches to a combination circuit.
  • Each is identified and reduced to an equivalent resistance, and these are further reduced until a single equivalent resistance is reached.

• Resistors in Parallel

  • The total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances.
  • Resistors are in parallel when each resistor is connected directly to the voltage source by connecting wires having negligible resistance.
  • This implies that the total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances.
  • Three resistors connected in parallel to a battery and the equivalent single or parallel resistance.
  • Calculate the total resistance in the circuit with resistors connected in parallel

• Resisitors in Series

  • The total resistance in the circuit with resistors connected in series is equal to the sum of the individual resistances.
  • The simplest combinations of resistors are the series and parallel connections.
  • This implies that the total resistance in a series is equal to the sum of the individual resistances.
  • Since all of the current must pass through each resistor, it experiences the resistance of each, and resistances in series simply add up.
  • Three resistors connected in series to a battery (left) and the equivalent single or series resistance (right).

• Charging a Battery: EMFs in Series and Parallel

  • When voltage sources are connected in series, their emfs and internal resistances are additive; in parallel, they stay the same.
  • When two voltage sources with identical emfs are connected in parallel and also connected to a load resistance, the total emf is the same as the individual emfs.
  • But the total internal resistance is reduced, since the internal resistances are in parallel.
  • Two voltage sources with identical emfs (each labeled by script E) connected in parallel produce the same emf but have a smaller total internal resistance than the individual sources.
  • Compare the resistances and electromotive forces for the voltage sources connected in the same and opposite polarity, and in series and in parallel

• Summary

  • The three types of equivalence (structural, automorphic, and regular) have progressively less strict definitions of what it means for two actors to be "equivalent."
  • Structural equivalence is the most "concrete" form of equivalence.
  • Pure structural equivalence can be quite rare in social relations, but approximations to it may not be so rare.
  • Automorphic equivalence is a bit more relaxed.
  • With automorphic equivalence, we are searching for classes of actors who are at the same distance from other sets of actors -- that is, we are trying to find parallel or substitutable sub-structures (rather than substitutable individuals).

• Automorphic equivalence

  • Even though actor B and actor D are not structurally equivalent (they do have the same boss, but not the same workers), they do seem to be "equivalent" in a different sense.
  • These are different people, but the two managers seem somehow equivalent.
  • In fact, actors B and D form an "automorphic" equivalence class.
  • The idea of automorphic equivalence is that sets of actors can be equivalent by being embedded in local structures that have the same patterns of ties -- "parallel" structures.
  • Note that the less strict definition of "equivalence" has reduced the number of classes.

• How Skeletal Muscles Are Named

  • The anatomical arrangement of skeletal muscle fascicles can be described as parallel, convergent, pennate, or sphincter.
  • Parallel muscles are characterized by fascicles that run parallel to one another, and contraction of these muscle groups acts as an extension of the contraction of a single muscle fiber.
  • Parallel muscles can be divided into fusiform and non-fusiform types based on their shape.
  • The biceps brachii is an example of a  fusiform parallel muscle, and is responsible for flexing the forearm.
  • Skeletal circular muscles are different from smooth muscle equivalents due to their structure and because they are under voluntary control

• Repetition and Parallelism

  • Repetition and parallelism can add clarity and dramatic punch to your speech.
  • Similarly, parallelism is a structured use of repetition by using identical or equivalent constructions in corresponding clauses to express the same sentiment.
  • Parallelism is an especially effective technique to provide structure, order, and balance in your speech, in addition to clarifying your argument.
  • Parallelism works the same way but without rote repetition of words or ideas and instead constructs them from similar examples.
  • See below how parallelism was used in these two speakers:

• Voltmeters and Ammeters

  • In order for a voltmeter to measure a device's voltage, it must be connected in parallel to that device .
  • This is necessary because objects in parallel experience the same potential difference.
  • The total resistance must be:
  • The same galvanometer can also function as an ammeter when it is placed in parallel with a small resistance R, often called the shunt resistance.
  • Since R and r are in parallel, the voltage across them is the same.