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4.4: Ohm's "Law" -- A Constitutive Relation

  • Page ID
    81491
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    One of the most frequently used constitutive relationships in studying electrical phenomena is referred to as Ohm's Law. This, like every constitutive relationship, is not really a law but a well-worn and useful model for a specific physical phenomenon.

    Ohm's Law relates three circuit variables: current, voltage, and resistance. For purposes of our discussion here, we will define voltage at a point \(\mathrm{A}\) with respect to a reference point \(\mathrm{N}\) as the value read by a "voltmeter" connected between the two points. The voltage at point \(A\) will be given the symbol \(V_{\mathrm{AN}}\) to remind us that every voltage reading is always measured with respect to some reference, e.g. point \(\mathrm{N}\). A typical system is shown in Figure \(\PageIndex{1}\).

    A wire connects point A and point B, passing through a resistor. A current i_A enters the resistor from point A, and a current i_B exits the resistor, going to point B. Point N, not attached to the wire, is connected to ground. A system consists of the resistor and the sections of wire immediately beside each of its ends.

    Figure \(\PageIndex{1}\): A system consisting of a resistor within a physical circuit.

    Empirical evidence for lumped circuit resistors shows that (1) there is no accumulation of charge in the resistor and (2) the current flowing through the resistor is related to the voltage change across a resistor by the following equation:

    \[V_{\mathrm{AN}} - V_{\mathrm{BN}} = iR \nonumber \]

    where

    • \(V_{A N}\) is the voltage at point A measured with reference to ground N, in volts
    • \(V_{B N}\) is the voltage at point B measured with reference to ground N, in volts
    • \(i\) is the electrical current flowing from point A \(\rightarrow\) B, in amperes
    • \(R\) is the electrical resistance, in ohms where \(1\, \text{volt} = (1 \mathrm{~A}) \times (1 \mathrm{\ ohm})\)

    Equation \(\PageIndex{1}\) is known as Ohm's Law and the various terms in the equation are shown in Figure \(\PageIndex{1}\). In a resistor, the magnitude of the voltage always decreases in the direction of the current flow, i.e. current flows inside a resistor from a high voltage to a lower voltage.


    This page titled 4.4: Ohm's "Law" -- A Constitutive Relation is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Donald E. Richards (Rose-Hulman Scholar) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.