R2S: Laws of Ohm & Joule

ELECTRICAL QUANTITIES

1. The Ohm

Electrical Resistance (symbol: R) is the opposition to the rate of flow of charges. Its S.I. unit of measurement is the Ohm (units: Ω), which was named in honor of key contributions of George Simon Ohm.

Definition: 1 ohm is the resistance of a material that carries a current of 1 ampere when a p.d. of 1 volt is applied.

2. Ohm’s Law

Experimentally, George Ohm found direct proportionality between the resulting current (I) through a metallic conductor to that of the imposed potential difference (V) across the conductor. That is:

The constant of proportionality is called conductance, G (in mhos), which is the reciprocal of resistance. Hence,

This mathematically represents Ohm’s law for a metallic conductor at constant temperature. Any material that obeys this law is said to be “ohmic,” signifying a linear correlation between the current (I) and the applied voltage (V) with, critically, direct proportionality. For example:

\begin{array}{l} I \propto V \\ \Rightarrow I = constant \times V \end{array}

\begin{array}{l} \frac{1}{R} = V \\ \Rightarrow V = I R \end{array}

\begin{array}{l} P = I^{2} R \\ = \frac{V^{2}}{R} \end{array}

\begin{array}{l} P = \frac{Δ W}{Δ t} \\ = \frac{V Δ Q}{Δ t} if V is constant \\ = V I \end{array}

Resistance, Power, Time

3. Joule’s Law

Definition: When a 1 ohm resistor carries a current of 1 ampere of current and its potential difference is 1 volt, it will dissipate 1 joule of energy in 1 second.

This gives rise to Joule’s Law. A simplified derivation is as follows:

Using Ohm’s Law, 2 variants of Joule’s Law are as follows:

In a resistor, electrical energy is primarily converted to thermal energy, which is dissipated as heat!

4. Summary - Ohm’s & Joule’s

The general relationships among the physical quantities of charge, current, voltage (potential, p.d. and e.m.f.) and power are intertwined. A unifying diagram is:

Caution! W as an S.I. unit is ‘the Watt’ for Power. But, as a symbol, W denotes Work in Joules, J.

\begin{array}{l} S.I. Units: \\ 1 W = 1 V \cdot A \end{array}

\begin{array}{l} S.I. Units \\ 1 W = 1 A^{2} \cdot Ω \\ 1 W = 1 V^{2} \cdot Ω^{-1} \end{array}

Review Keynotes:

• Elec. Symbols & Tables
• Significant Figures