3.4 O HM ’ S L AW

. O HM ’ S L AW A basic law regarding flow of currents was discovered by G.S. Ohm in , long before the physical mechanism responsible for flow of currents was discovered. Imagine a conductor through which a current I is flowing and let V be the potential difference between the ends of the conductor. Then Ohm’s law states that V ∝ I or, V = R I ( . ) where the constant of proportionality R is called the resistance of the conductor. The SI units of resistance is ohm , and is denoted by the symbol Ω . The resistance R not only depends on the material of the conductor but also on the dimensions of the conductor. The dependence of R on the dimensions of the conductor can easily be determined as follows. Consider a conductor satisfying Eq. ( . ) to be in the form of a slab of length l and cross sectional area A [Fig. . (a)]. Imagine placing two such identical slabs side by side [Fig. . (b)], so that the length of the combination is l . The current flowing through the combination is the same as that flowing through either of the slabs. If V is the potential difference across the ends of the first slab, then V is also the potential difference across the ends of the second slab since the second slab is FIGURE . Charges + Q and – Q put at the ends of a metallic cylinder. The electrons will drift because of the electric field created to neutralise the charges. The current thus will stop after a while unless the charges + Q and – Q are continuously replenished. FIGURE . Illustrating the relation R = ρ l / A for a rectangular slab of length l and area of cross-section A . identical to the first and the same current I flows through both. The potential difference across the ends of the combination is clearly sum of the potential difference across the two individual slabs and hence equals V . The current through the combination is I