Electric Potential

Electric potential at a point A in an electric field is the work done per unit positive charge in transporting it from infinitely far away to the point A. (see figure) 

$V=\frac{\mathrm{W}}{{\mathrm{Q}}_0}$

You need a potential difference (p. d.) to ‘push’ current around and electric circuit. Potential difference is also called voltage. Figure shows marbles on a ramp. This can be used as a model for potential difference. On a flat surface the marbles won’t move but when there is a height difference they can roll down the ramp. Similarly, electrons will flow when a potential difference is applied across a component.

Electric potential is a scalar quantity. 

It can be positive or negative.

1.0Unit of Electric Potential

SI unit : Volt (V)

1 Volt = 1 Joule/coulomb = 1 J C^–1

Definition of 1 volt in terms of electric potential

1 volt is the electric potential at any point A when 1 joule work is done in moving a charge of 1 coulomb from infinity to the point A.

2.0Potential Difference

Potential difference between two points is defined as the work done in carrying a unit positive charge from one point to another point. (see Figure)

$V=\frac{\mathrm{W}}{{\mathrm{Q}}_0}$

Definition of 1 Volt in Terms of Potential Difference

1 volt is the potential difference between two points when 1 joule work is done in moving a charge of 1 coulomb from one point to another.

If work done in moving a unit positive charge from point A to point B is zero, it means, potentials of point A and point B are same,i.e.,$V_A=V_B$

The potential difference between two points is independent of the actual path followed between the points.

Figure below shows how energy is transferred in a circuit. The cell transfers energy to the charge, and so the charge then has the potential to transfer energy to other components in the circuit. the charge has ‘potential energy’.

Exponent form of a number

The mass of an electron is 9.1 × 10^–31 kg and the charge of an electron is 1.6 × 10^-19 coulomb. Today the world population is around 7000000000 or 7×10⁹. Can you read these numbers?

To express these large numbers in a form, which can be read, written, compared easily, we use the exponent form.

3.0Laws of Exponents

Multiplication or Product Rule

Rule 1 : When the numbers have the same base 'a' such that a is a non-zero rational number and m and n are integer numbers then

$a^m\times a^n=a^{m+n}$

Example :

Simplify $x^6\times x^{-9}$

Solution : $x^6\times x^{-9}=x^{6-9}=x^{-3}$

Rule 2 : If 'a' is a rational number and 'm' and 'n' are the integers, then

$(a^m{)}^n=a^{mn}$

Rule 3 : If 'a' and 'b' are rational numbers and m is an integer then

${}^{}(a\times b{)}^m=a^m\times b^{m}Or{}^{}(ab{)}^m=a^m\times b^m$

Example :

Simplify $(3a^2{b}^4{)}^4$

Solution : $(3a^2{b}^4{)}^4=(3^4{a}^8{b}^{16}{)}^{=81a8b16}$

Division Rule

Rule 1 : If 'a' is a rational number and a ≠ 0 and 'm' and 'n' are the integers numbers, then

$a^m÷a^n=a^{m-n}$

Example-1 : Simplify

(i) $(3\times 2^3{)}^2$

(ii) $3^7{\times }^{{\left(\frac{2}{3}\right)}^7}$

Solution : $3^2\times 2^6=9\times 64=576$

Example-2 : Simplify

(i) $\frac{(-2{)}^7}{(-2{)}^{12}}$

(ii) $(-\frac{3}{4}{)}^4÷(-\frac{3}{4}{)}^2$

Solution : (i) $\frac{(-2{)}^7}{(-2{)}^{12}}=(-2{)}^{7-12}=(-2{)}^{-5}$

(ii) $(-\frac{3}{4}{)}^4÷(-\frac{3}{4}{)}^2=(-\frac{3}{4}{)}^{4-2}=(-\frac{3}{4}{)}^2$

Also Read