Resistor

Calculations

Ohm's law

The relationship between voltage, current, and resistance through an object is given by a simple equation which is called Ohm's Law:

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:V = I cdot R

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where V is the voltage across the object in volts (in Europe, U), I is the current through the object in amperes, and R is the resistance in ohms. (In fact this is only a simplification of the original Ohm's law - see the article on that law for further details.) If V and I have a linear relationship -- that is, R is constant -- along a range of values, the material of the object is said to be ohmic over that range. An ideal resistor has a fixed resistance across all frequencies and amplitudes of voltage or current.

Related Topics:
Volt - Ampere - Ohm

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Superconducting materials at very low temperatures have zero resistance. Insulators (such as air, diamond, or other non-conducting materials) may have extremely high (but not infinite) resistance, but break down and admit a larger flow of current under sufficiently high voltage.

Related Topics:
Superconducting - Air - Diamond

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Power dissipation

The power dissipated by a resistor is the voltage across the resistor times the current through the resistor:

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:P = I cdot V = I^2 R = rac{V^2}{R}

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All three equations are equivalent, the last two being derived from the first by Ohm's Law.

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The total amount of heat energy released per unit time is the integral of the power:

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:

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W = int_{t_1}^{t_2} v(t) i(t), dt

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If the average power dissipated exceeds the power rating of the resistor, then the resistor will first depart from its nominal resistance, and will then be destroyed by overheating.

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Series and parallel circuits

Resistors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent resistance (Req):

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:

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: rac{1}{R_{eq}} = rac{1}{R_1} + rac{1}{R_2} + cdots + rac{1}{R_n}

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The parallel property can be represented in equations by two vertical lines "||" (as in geometry) to simplify equations. For two resistors,

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: R_{eq} = R_1 | R_2 = {R_1 R_2 over R_1 + R_2}

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The current through resistors in series stays the same, but the voltage across each resistor can be different. The sum of the potential differences (voltage) is equal to the total voltage. To find their total resistance:

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:

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: R_{eq} = R_1 + R_2 + cdots + R_n

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A resistor network that is a combination of parallel and series can sometimes be broken up into smaller parts that are either one or the other. For instance,

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:

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: R_{eq} = left( R_1 | R_2 ight) + R_3 = {R_1 R_2 over R_1 + R_2} + R_3

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However, many resistor networks cannot be split up in this way. Consider a cube, each edge of which has been replaced by a resistor. Determining the resistance between (say) two opposite vertices requires matrix methods for the general case. However, if all twelve resistors are equal, the corner-to-corner resistance is 5/6 of any one of them.

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