Resistance

A resistor is a two-terminal electronic component that produces a voltage across its terminals that is proportional to the electric current through it in accordance with Ohm's law:

V = IR

Resistors are elements of electrical networks and electronic circuits and are ubiquitous in most electronic equipment. Practical resistors can be made of various compounds and films, as well as resistance wire (wire made of a high-resistivity alloy, such as nickel/chrome).

The primary characteristics of a resistor are the resistance, the tolerance and the power rating. Other characteristics include temperature coefficient, noise, and inductance. Less well-known is critical resistance, the value below which power dissipation limits the maximum permitted current flow, and above which the limit is applied voltage. Critical resistance depends upon the materials constituting the resistor as well as its physical dimensions; it's determined by design.

Resistors can be integrated into hybrid and printed circuits, as well as integrated circuits. Size, and position of leads (or terminals) are relevant to equipment designers; resistors must be physically large enough not to overheat when dissipating their power.

The electrical resistance of an object is a measure of its opposition to the passage of a steady electric current. An object of uniform cross section will have a resistance proportional to its length and inversely proportional to its cross-sectional area, and proportional to the resistivity of the material.
Discovered by Georg Ohm in the late 1820s,[1] electrical resistance shares some conceptual parallels with the mechanical notion of friction. The SI unit of electrical resistance is the ohm, symbol Ω. Resistance's reciprocal quantity is electrical conductance measured in siemens, symbol S.
The resistance of a resistive object determines the amount of current through the object for a given potential difference across the object, in accordance with Ohm's law:
where
R is the resistance of the object, measured in ohms, equivalent to J·s/C2
V is the potential difference across the object, measured in volts
I is the current through the object, measured in amperes
For a wide variety of materials and conditions, the electrical resistance does not depend on the amount of current through or the amount of voltage across the object, meaning that the resistance R is constant for the given temperature. Therefore, the resistance of an object can be defined as the ratio of voltage to current:
In the case of nonlinear objects (not purely resistive, or not obeying Ohm's law), this ratio can change as current or voltage changes; the ratio taken at any particular point, the inverse slope of a chord to an I–V curve, is sometimes referred to as a "chordal resistance" or "static resistance"

Resistance in a Parallel CircuitIn the example diagram, figure 3-44, there are two resistors connected in parallel across a 5-volt battery. Each has a resistance value of 10 ohms. A complete circuit consisting of two parallel paths is formed and current flows as shown.Figure 3-44. - Two equal resistors connected in parallel.Computing the individual currents shows that there is one-half of an ampere of current through each resistance. The total current flowing from the battery to the junction of the resistors, and returning from the resistors to the battery, is equal to 1 ampere.The total resistance of the circuit can be calculated by usingthe values of total voltage (ET) and total current (IT).NOTE: From this point on the abbreviations and symbology for electrical quantities will be used in example problems.Given:Solution:This computation shows the total resistance to be 5 ohms; one-half the value of either of the two resistors.Since the total resistance of a parallel circuit is smaller than any of the individual resistors, total resistance of a parallel circuit is not the sum of the individual resistor values as was the case in a series circuit. The total resistance of resistors in parallelis also referred to as EQUIVALENT RESISTANCE (Req). The terms total resistance and equivalent resistance are used interchangeably. There are several methods used to determine the equivalent resistance of parallel circuits. The best method for a given circuit depends on the number and value of the resistors. For the circuit described above, where all resistors have the same value, the following simple equation is used:This equation is valid for any number of parallel resistors of EQUAL VALUE.Example. Four 40-ohm resistors are connected in parallel. What is their equivalent resistance?Given:Solution:Figure 3-45 shows two resistors of unequal value in parallel. Since the total current is shown, the equivalent resistance can be calculated.Figure 3-45. - Example circuit with unequal parallel resistors.Given:Solution:The equivalent resistance of the circuit shown in figure 3-45 is smaller than either of the two resistors (R 1, R2). An important point to remember is that the equivalent resistance of a parallel circuit is always less than the resistance of any branch.

Equivalent resistance can be found if you know the individual resistance values and the source voltage. By calculating each branch current, adding the branch currents to calculate total current, and dividing the source voltage by the total current, the total can be found. This method, while effective, is somewhat lengthy. A quicker method of finding equivalent resistance is to use the general formula for resistors in parallel:If you apply the general formula to the circuit shown in figure 3-45 you will get the same value for equivalent resistance (2Ω) as was obtained in the previous calculation that used source voltage and total current.Given:Solution:Convert the fractions to a common denominator.Since both sides are reciprocals (divided into one), disregard the reciprocal function.The formula you were given for equal resistors in parallelis a simplification of the general formula for resistors in parallel There are other simplifications of the general formula for resistors in parallel which can be used to calculate the total or equivalent resistance in a parallel circuit.RECIPROCAL METHOD. - This method is based upon taking the reciprocal of each side of the equation. This presents the general formula for resistors in parallel as:This formula is used to solve for the equivalent resistance of a number of unequal parallel resistors. You must find the lowest common denominator in solving these problems. If you are a little hazy on finding the lowest common denominator, brush up on it in Mathematics Volume 1, NAVEDTRA 10069 (Series).Example: Three resistors are connected in parallel as shown in figure 3-46. The resistor values are: R1 = 20 ohms, R2 = 30 ohms, R3 = 40 ohms. What is the equivalent resistance? (Use the reciprocal method.)Figure 3-46. - Example parallel circuit with unequal branch resistors. Given:Solution:PRODUCT OVER THE SUM METHOD. - A convenient method for finding the equivalent, or total, resistance of two parallel resistors is by using the following formula.This equation, called the product over the sum formula, is used so frequently it should be committed to memory.Example. What is the equivalent resistance of a 20-ohm and a 30-ohm resistor connected in parallel, as in figure 3-47?Figure 3-47. - Parallel circuit with two unequal resistors.Given:Solution:Four equal resistors are connected in parallel, each resistor has an ohmic value of 100 ohms, what is the equivalent resistance?Three resistors connected in parallel have values of 12 kΩ, 20 kΩ, and 30 kΩ. What is the equivalent resistance?Two resistors connected in parallel have values of 10 kΩ and 30 kΩ.