## Electric Current and Ohm’s Law Units Of Different Electrical Quantities

**Unit of electric charge:** The si unit of charge is coulomb (C). The amount of charge that deposits 0.001118 g of silver on the cathode by electrolyzing silver nitrate solution is called 1 coulomb.

CGS or Gaussian unit of electric charge is esu of charge or statcoulomb (statC).

1 C = 3 x 10^{9} esu charge or simply, esu

By the way, the charge of an electron,

e = 1.6 X 10^{-19} C = 4.8 x 10^{-10} esu

**Unit of current:** The unit of current in SI is ampere (A).

A current of 1 A is fairly large. So smaller units are generally used milliampere (1 mA = 10^{-3} A) and microampere (1ΩA = 10^{-6}A).

CGS unit of current is esu of current or statampere (stat A).

1 A = 3 X 10^{9} esu current or simply, esu

**Read and Learn More Class 12 Physics Notes**

Another unit of current is emu of current or abamp.

1 abamp = 1 emu current = c x 1 esu current

= 3 x 10^{10} esu current = 10 A

Here, velocity of light in vacuum = c = 3 x 10^{10} cm.s^{-1}

**Unit of potential difference:**

The unit of electrical potential or potential difference in SI is volt (V). For very low and very high potential differences millivolt (1 mV = 10-3V) and kilovolt (lkV = 103V) are used respectively.

CGS unit ofpotential is esu ofpotential or statvolt (statV).

1 V = \(\frac{1}{300}\) esupotential

Another unit of potential difference is the emu of potential or a bvolt.

1 abvolt = 1 emu potential = \(\frac{1}{3 \times 10^{10}}\) potential

= 10^{-8}V

**Unit Of resistance:** The unit of resistance in SI is ohm (Ω). As 1 n resistance is considerably low, comparatively bigger units are often required. The units commonly used are kiloohm (\(1 \mathrm{k} \Omega=10^3 \Omega\)) and megaohm (\(1 \mathrm{M} \Omega=10^6 \Omega\)).

The CGS or Gaussian unit of resistance is esu of resistance or statohm (statΩ).

⇒ \(1 \Omega=\frac{1 \mathrm{~V}}{1 \mathrm{~A}}=\frac{\frac{1}{300}}{3 \times 10^9} \text { esu resistance }\)

⇒ \(\frac{1}{9} \times 10^{-11} \text { esu resistance }\)

= 1.1 x 10^{-12} esuresistance

Another unit of resistance is emu of resistance or abohm.

1 abohm = 1 emu resistance = \(\frac{ 1 emu potential}{1 emu current}\)

⇒ \(\frac{10^{-8} \mathrm{~V}}{10 \mathrm{~A}}\)

= \(10^{-9} \Omega\)

or, 1 Ω = 10^{9} emu resistance

**International Definitions of Coulomb, Ampere, Volt and Ohm:**

**International coulomb:** The coulomb is the quantity of electricity carried in 1 s by a current of 1 A.

**International ampere:** 1 A is defined as the constant current that will produce an attractive force of 2 x 10^{-7} N per meter of length between two straight, parallel conductors of infinite length and negligible circular cross-section placed 1 m apart in a vacuum.

**International volt:** 1 V is \(\frac{1}{1.01830}\) of the emf of a standard Weston cadmium cell at 20°C.

**International ohm:** It is the resistance of a column of mercury of length 106.3 cm, cross-sectional area 1 mm^{2}, and mass 14.4521 g kept at the melting point of ice (0°C).

In SI, an ampere Is a fundamental unit. All other units of electricity are derived units. Other units can be derived if the definition of ampere is known.

**For Example,**

coulomb = ampere x second volt = \(\frac{\text { Joule }}{\text { coulomb }}\)

ohm = \(\frac{\text { volt }}{\text { ampere }}\)