DC Circuit

Electric Current


​Electric current is produced due to the flow of electric charges. Its magnitude is measured by the flow of charges in one second. Hence, the rate of flow of charges is called electric current. It is denoted by $I$ or $i$.

If $q$ amount of charge flow in time $t$ sec, then, \[\text{Electric Current (I)}=\frac{\text{Amount of charges flow (q)}}{\text{Time taken (t)}}\] \[I=\frac{q}{t}\] The S.I. unit of current is $\text{Coulomb}$ per $\text{second}$ which is called Ampere.

\[1\;\text{A}=1\;\text{Cs}^{-1}\] Charge of one electron is $1.6×10^{-19}\;\text{C}$. Then, for one Coulomb, \[\text{Number of electrons}=\frac{1}{1.6×10^{-19}}=6.25×10^{18}\] Thus, current is said to be one ampere in a circuit if $6.25×10^{18}$ electrons flow per second across the conductor.

[Also See: Coulomb’s Law]

If $∆q$ is the net amount of charge that passes through any cross section in time interval $∆t$, then, average current is, \[I_{\text{av}}=\frac{∆q}{∆t}\] And, instantaneous current $(I)$ is, \[I=\lim_{∆t \to 0}\frac{∆q}{∆t}=\frac{dq}{dt}\]

Since charge is conserved, current flowing through the conductor is same i.e. the amount of charge entering at one end per second of a conductor is equal to the amount of charge leaving at another end per second of the conductor. Hence, current does not change in any cross section of the conductor and the conductor remains uncharged when current flows through it.

Charge Carriers In Different Conductors

  • In a metallic conductor, charge carriers are free electrons. The electrons in a metallic conductor flow in a particular direction and constitute current. In a semiconductor, charge carriers are electrons as well as holes.
  • In liquid, charge carriers are positively and negatively charged ions. All liquids cannot conduct charges. Those liquids which conduct charge are called electrolytes. When NaCl is dissolved in water, NaCl gets ionized into Na⁺ and Cl⁻. On applying p.d. between any two points of the solution, Na⁺ ions move towards the negative terminal and Cl⁻ moves towards positive terminal which conducts electric current.
  • In gases, charge carriers are ions and electrons.
  • In plasma, charge carriers are both electrons and ions.

Direction of Current

​When the chemical cell was discovered (at the beginning of 10th century), it was assumed that the flow of current is due to the flow of positive charge from positive terminal of the battery to the negative terminal of it. But when electron was discovered, it was proved that flow of current is due to the flow of negative charge from negative terminal of a battery to the positive terminal of it. We follow the old rule and show the direction of current from positive to negative terminal of cell and the current is known as conventional current. The direction of flow of electrons gives the direction of electronic current.

Direction of Current

Types of Electric Current

1. Direct Current or Steady Current

A current whose magnitude and direction does not change with time is known as direct current.

Direct Current

2. Varying Current

A current whose magnitude changes but direction remains same with time is known as varying current.

Varying Current

3. Alternating Current

A current whose magnitude and direction changes periodically is called alternating current.

Alternating Current

Current is a scalar quantity

​Current is not a vector quantity because it does not obey law of vector addition. Current does not have direction because the current in the wire does not change if the wire is bent or tied.

Current is a scalar quantity

​In the above figure, current in wire $OC$ is $7A$ (vector sum will be $5A$). Since current does not follow triangle law of vector addition, so it is a scalar quantity.

[Also See: Scalars and Vectors]

Mechanism of Metallic Conduction

​There are some free electrons in metals. Free electrons are those electrons which are not attached to the orbits of the atom or are loosely bound in metals. These free electrons collide with other electrons or ions. Due to the collisions, they are in random motion. They are randomly distributed in all directions. In any cross section of the conductor, the rate at which they pass through it from left to right is same as they pass through it from right to left. Hence, net rate flow of electrons is zero and no current is constituted in the conductor.

Mechanism of Metallic Conduction figure (1)

​When electric field is applied in the conductor, the electrons move in a particular direction and hence it constitutes the current. The electric force accelerates the electrons. The electrons keep colliding; gaining and losing their kinetic energy. Hence, they alternately stop and accelerate. The average velocity of the electrons is considered which is known as drift velocity.

Mechanism of Metallic Conduction figure (2)

Expression for Drift Velocity

​Consider a metallic conductor of length $l$ and cross sectional area $A$ having number of electrons per unit volume $n$.

Expression for Drift Velocity

​Let $N$ be the total number of electrons of the conductor. Then, \[N=n×\text{Volume}\] \[N=n×l×A\text{ __(1)}\] Let $I$ be the current flowing through the conductor. Then, \[I=\frac{q}{t}\] Where, $q$ is the total number of charge and $t$ is the time taken by a charge to move from one end of the conductor to another end. \[I=\frac{Ne}{t}\text{ __(2)}\]

If the conventional direction of current is right to left then, electrons are moving from left to right. Let the electrons be moving with drift velocity $v$. Then, \[v=\frac{l}{t}\] \[t=\frac{l}{v}\text{ __(3)}\] From $(1)$, $(2)$ and $(3)$, \[I=nlAe\frac{v}{l}\] \[I=nAev\] \[v=\frac{I}{nAe}\] This is the expression for drift velocity of the electrons.

Current Density

​Current per unit cross sectional area is called current density. It is denoted by $J$. \[J=\frac{I}{A}\] Its S.I. unit is $\text{Am}^{-2}$. Current density is a vector quantity which direction is the direction of the conventional current. For the direction of moving electrons, current density is $-J$.