series equivalent resistance

Examples of series 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:
  • As a special case, the resistance of N resistors connected in series, each of the same resistance R, is given by NR.Resistors in a parallel configuration are each subject to the same potential difference (voltage), however the currents through them add.
  • 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.
  • One practical application of these relationships is that a non-standard value of resistance can generally be synthesized by connecting a number of standard values in series or parallel.

• Combination Circuits

  • In that case, wire resistance is in series with other resistances that are 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.
  • Essentially, wire resistance is a series with the resistor.
  • Each is identified and reduced to an equivalent resistance, and these are further reduced until a single equivalent resistance is reached.

• Resisitors in Series

  • The total resistance in the circuit with resistors connected in series is equal to the sum of the individual resistances.
  • 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).
  • Calculate the total resistance in the circuit with resistors connected in series

• Resistors in Parallel

  • The total resistance in a parallel circuit is equal to the sum of the inverse of each individual resistances.
  • Resistors in a circuit can be connected in series or in parallel.
  • In a series circuit, the two light bulbs would be half as dim when connected to a single battery source.
  • In a series circuit, the battery would last just as long as it would with a single light bulb, only the brightness is then divided amongst the bulbs.
  • Three resistors connected in parallel to a battery and the equivalent single or parallel resistance.

• The Loop Rule

  • Another equivalent statement is that the algebraic sum of the products of resistances of conductors (and currents in them) in a closed loop is equal to the total electromotive force available in that loop.
  • illustrates the changes in potential in a simple series circuit loop.
  • The emf supplies 18 V, which is reduced to zero by the resistances, with 1 V across the internal resistance, and 12 V and 5 V across the two load resistances, for a total of 18 V.
  • (a) In this standard schematic of a simple series circuit, the emf supplies 18 V, which is reduced to zero by the resistances, with 1 V across the internal resistance, and 12 V and 5 V across the two load resistances, for a total of 18 V.
  • (b) This perspective view represents the potential as something like a roller coaster, where charge is raised in potential by the emf and lowered by the resistances.

• 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 voltage sources are in series facing the same direction, their internal resistances add and their electromotive force, or emf, add algebraically.
  • The disadvantage of series connections of cells in this manner, though, is that their internal resistances add.
  • This schematic represents a flashlight with two cells (voltage sources) and a single bulb (load resistance) in series.
  • Compare the resistances and electromotive forces for the voltage sources connected in the same and opposite polarity, and in series and in parallel

• Power

  • Power delivered to an RLC series AC circuit is dissipated by the resistance in the circuit, and is given as $P_{avg} = I_{rms} V_{rms} cos\phi$.
  • Power delivered to an RLC series AC circuit is dissipated by the resistance alone.
  • The forced but damped motion of the wheel on the car spring is analogous to an RLC series AC circuit.
  • Phasor diagram for an RLC series circuit.
  • Calculate the power delivered to an RLC-series AC circuit given the current and the voltage

• What Is Cash?

  • Cash and cash equivalents are the most liquid type of company assets used by businesses to settle debts and purchase goods.
  • Cash equivalents are also generally included with cash on a business's financial statements.
  • For an investment to be considered a "cash equivalent," it must mature within three months.
  • Since cash can also easily be stolen or mishandled, it is important to maintain a strict series of internal controls to ensure that these assets are not lost.
  • Define the role cash or cash equivalents play within a business

• Acetyl CoA and the Citric Acid Cycle

  • The citric acid cycle, shown in —also known as the tricarboxylic acid cycle (TCA cycle) or the Krebs cycle—is a series of chemical reactions used by all aerobic organisms to generate energy through the oxidation of acetate—derived from carbohydrates, fats, and proteins—into carbon dioxide.
  • Acetyl-CoA along with two equivalents of water (H2O) are consumed by the citric acid cycle, producing two equivalents of carbon dioxide (CO2) and one equivalent of HS-CoA.
  • In addition, one complete turn of the cycle converts three equivalents of nicotinamide adenine dinucleotide (NAD+) into three equivalents of reduced NAD+ (NADH), one equivalent of ubiquinone (Q) into one equivalent of reduced ubiquinone (QH2), and one equivalent each of guanosine diphosphate (GDP) and inorganic phosphate (Pi) into one equivalent of guanosine triphosphate (GTP).
  • The citric acid cycle, or Krebs cycle, is a series of chemical reactions used by all aerobic organisms to generate energy through the oxidization of acetate—derived from carbohydrates, fats, and proteins—into carbon dioxide.

• Voltmeters and Ammeters

  • A galvanometer can function as a voltmeter when it is connected in series with a large resistance R.
  • The total resistance must be:
  • For other voltage ranges, other resistances are placed in series with the galvanometer.
  • Many meters allow a choice of scales, which involves switching an appropriate resistance into series with the galvanometer.
  • An ammeter (A) is placed in series to measure current.