ELECTRIC CURRENT Part-1

Electric Current

Electric Charges: 

• Electric Charge is the number of electrons or amount of energy that can be transferred from one body to another body.

• Electric Charges can be classified into TWO types, they are Positive Charge and Negative Charge. Positive charges are Protons and Negative charges are Electrons. These charges are equal in magnitude and can neither be created nor destroyed but moves from one body to the other.

• The best example of electric charge is Lightning which is an electric discharge between two clouds or between cloud and earth. This electric discharge in the air appears to be an electric spark or lightning.

• 

Electric Current: (Drude & Lorentz Theory)

Drude and Lorentz, scientists of the 19th century stated that the metal conductors consists of both positive and negative ions, where positive ions are fixed at some locations in the conductor known as Lattice and negative ions move in a random motion i.e., move in any direction if it is an open circuit (not connected to any source or battery). The net charge moving in the conductor through any cross-section is Zero.

When the conductor is connected to the battery through a bulb, then the bulb glows as the energy transfer takes place from the battery to the bulb.

As electrons are responsible for the transfer of energy, hence the electric current is defined as

• Electric Current is an Ordered motion of electrons or negative charges in a conductor.
• Electric Current is defined as the amount of charge crossing any cross-section of the conductor in one second.
• It is denoted by the letter 'I'.
• The SI unit of the Electric Current is Ampere (A).
• Ammeter is the device to measure the electric current.

• Formula: Electric Current (I) = electric charge / time interval i.e., I = Q / t

• Formula in units: 1 Ampere = 1 coloumb / 1 second i.e., 1A = 1C / 1s ,             where 1 Coloumb = 6.625 × 10¹⁸ electrons.

Drift Speed (v_d):

Definition: Electrons move with a constant average speed in the conductor, we refer to this speed as drift speed or drift velocity.

Consider the conductor with cross-section area 'A' and the ends of the conductor are connected to the terminals of the battery. Let 'v_d' be the distance travelled by each charge in one second. Then the volume of the conductor will be Av_d. The charge density (the number of charges present in the conductor per unit volume) be 'n'. Then the number of charges present in the conductor be nAv_d.

Thus, the electric current passing through the conductor or the total charge crossing any cross-section of the conductor can be calculated as

I = nqAv_d

Therefore, Drift Speed or Drift Velocity v_d = I / nqA

Example Problem:

Q1. Calculate the drift speed of electrons in a copper wire carrying a current of 1A and cross-section area A=10^-6m². The electron density of copper n=8.5×10²⁸m^-3. (assume q=e).

Sol: Given Data: 

        A=10^-6m²

            n=8.5×10²⁸m^-3

            ^{q = e =}1.602×10^-19

            v_{d = ?}

_{We know that drift speed,} 

 v_d = I / nqA

      = 1 / 8.5×10²⁸ ×1.602×10^-19 ×10^-6

        

      = 1 / 13.617×10³

       = 1 / 13617

       = 7.34×10^-5 m/s

  v_d = 0.07 mm/s

This drift velocity shows that electrons move very slowly.

Potential Difference:

When the ends of the conductor are connected to the terminals of the battery, an electric field is set up throughout the conductor. This electric field forces the electrons to move in a specific direction.

Definition: Work done by the electric field on a unit positive charge to move it from one point of the conductor to the other through a distance 'l' is called Potential Difference between those points. The potential difference is also called Voltage.

It is denoted by 'V'.

The SI unit of potential difference is 'Volt', and it is also denoted by 'V'.

Formula: V = W/q = F_el/q

Formula interms of units: 1Volt = 1 Joule / 1 Coloumb i.e., 1V=1J/1C

The direction of Electric charges and fields:

The positive and negative charges move in opposite directions if the electric current passes through the fluids.

In an electrolyte, the direction of motion of positive charges is always in the direction of the electric field and the direction of motion of negative charges or electrons is opposite to that of positive charges and electric field.

Thus positive and negative charges exist for conduction in fluids. But, in the case of metal conductors, there will be only the motion of electrons.

Electromotive Force (ᵋ):

Definition: Electromotive force is defined as the work done by the chemical force to move unit positive charge from negative terminal to positive terminal of the battery.

SI unit: volt

Formula: ᵋ = W/q = F_cd/q

where W - work done

            q - charge

            F_c - chemical force

             d - the distance between the ends of the conductor

Devices to measure electric current and potential difference and their connections in an electric circuit:

Electric Current: Ammeter and it is connected in series.

Potential Difference: Voltmeter and it is connected in parallel.

Battery/Cell and its working:

A battery or cell consists of two electrodes (metal plates) and an electrolyte (chemical). This electrolyte contains both positive and negative ions which move in opposite directions. They move in a specific direction when chemical force is applied to them. Based on the chemical's nature, positive ions move towards one plate, accumulate on it and negative ions move towards the other plate and also accumulate on it as shown in fig. no.6. This process of accumulation carries out till both the plates get sufficiently charged.

However, one plate becomes positively charged called an Anode and the other plate becomes negative charged called a Cathode.

At this point, positive and negative ions experience another force called an electric force in a direction opposite to the directions of chemical force. Here the magnitude of the electric force depends on the number of charges accumulated on the plates. The motion of ions towards their respective plates takes till the chemical force is stronger than the electric force as shown in fig.7

When chemical force is equal to the electric force, there is no motion of ions as shown in fig.no.8. 

Hence Battery/cell maintains the constant potential difference between its terminals.

Ohm's Law:

Definition: Ohm's law states that "the potential difference between the ends of a conductor is directly proportional to the electric current passing through it at constant temperature".

It is denoted by ohm

Formula: V=IR 

where V - Potential Difference

           I - Electric Current

           R - Resistance (constant)

The formula in terms of units: 1 ohm = 1 volt/1 Ampere

Lab Activity:

Aim: To show that the ratio V/I is constant for the conductor and also not constant for some materials.

Materials Required: 1 Voltmeter, 1 Ammeter, 5 dry cells of 1.5V each, conducting wires, switch/key, iron spoke or iron rod of length 10cm and LED.

Procedure:

Case-1: Iron spoke/Iron rod:

1. Connect the circuit as shown in the figure.
2. Connect the iron spoke to the ends of the conducting wires and then close the key.
3. Note down the readings of electric current and potential difference from ammeter and voltmeter.
4. Then connect one more cell i.e., two cells in series to the circuit and tabulate the readings.
5. Repeat the same procedure by adding 3 cells, 4 cells and 5 cells respectively.
6. Then find the V/I value for each case.

Observation: It can be observed that the value of V/I is constant i.e., V is directly proportional to I.

Case-2: LED:

1. In the same circuit, if we replace iron spoke with LED, it can be observed the ratio V/I is not constant.

The V-I graphs for each case can be:

Result: In case-1, the ratio of electric current and the potential difference is constant by assuming the temperature as constant whereas, in case-2, the ratio of electric current and the potential difference is not constant. Hence it can be concluded that the ratio of electric current and the potential difference is constant only for some materials at a constant temperature.

Ohmic & non-ohmic conductors:

Based on Ohm's law, materials can be classified as:

• Ohmic Materials: Materials that obeys ohm's law is known as ohmic materials.

        Eg: Metals

• Non-Ohmic Materials: Materials that do not obey ohm's law is known as non-ohmic materials.

Limitations of Ohm's Law:

• Ohm's law is valid for metal conductors when temperature and other physical conditions remain constant.
• Ohm's law is not valid for gaseous & semi-conductors like Germanium and Silicon.
• For changing temperature, the V/I graph is non-linear as the resistance of the material changes with temperature.