Plus Two Physics Notes Chapter 3 Current Electricity is part of Plus Two Physics Notes. Here we have given Plus Two Physics Notes Chapter 3 Current Electricity.

Board |
SCERT, Kerala |

Text Book |
NCERT Based |

Class |
Plus Two |

Subject |
Physics Notes |

Chapter |
Chapter 3 |

Chapter Name |
Current Electricity |

Category |
Plus Two Kerala |

## Kerala Plus Two Physics Notes Chapter 3 Current Electricity

**Simplified Detailed Notes**

**Electric Current
**The flow of charges consitutes an electric current.

Electric current, l =

SI unit of current is ampere (A). Current is a scalar quantity.

Conventionally the direction of current flow is taken to be the direction of flow of positive charge (opposite to flow of electrons).

**Ohm’s Law**

Ohm’s law states that the current flowing through a conductor is directly proportional to the potential difference across its ends, provided the temperature and other physical conditions are kept constant.

V ∝ I or V = IR

⇒ R = ; where R is called resistance.

**Resistance: **It is the property due to which a conductor opposes the flow of charges through it. It is equal to the ratio of the potential difference applied across the conductor to the cur-rent flowing through it. It depends on length and area of cross section as:

R = ρ ; ρ = resistivity of the material.

SI unit of resistance is ohm (Ω).

Note: If a wire is stretched, length increases but area decreases because volume remains constant. If conductor is stretched or compressed to n times the original length then,

l’ = nl ⇒ R’ = n^{2} R

**Resistivity: **It is defined as the resistance of the conductor of unit length and of unit area of cross section.

ρ =

SI unit of resistivity is ohm metre (Ω m).

It depends on nature of material and physical conditions like pressure, temperature etc.

**Conductance:** Reciprocal of resistance,

G =

SI unit: ohm^{-1} or mho or siemen (S).

**Conductivity:** It is the reciprocal of resistvity.

σ =

SI unit of conductivity is ohm^{-1}m^{-1} or Sm^{-1}

j = σ E

where j = current density and E = electric field.

**Limitations of Ohm’s Law**

- The relation between V and I is not linear.
- The relation between V and I depends on the sign of V.
- The relation between V and I is not unique. The substances which do not obey Ohm’s law are called non-Ohmic conductors.

**Temperature Dependence of Resistivity**

Temperature coefficient of resistance is defined as the ratio of increase in resistance to the original resistance per degree rise of temperature.

**For conductors:**as temperature increases, relaxation time T decreases. From the equation it is clear that resisitivity increases as temperature increases.**For semiconductors:**as temperature increases, number of free electrons in conduction band increases (n) while x decreases. But the increases in n is more than the decrease in x. Therefore as temperature increases resistivity decreases.**Uses of alloys:**They have high resistivity and low temperature coefficient. Thus they are useful for making standard resistors.**superconductivity:**The resisitivity of certain metal as alloy drops to zero when they are cooled below a certain temperature is called superconductivity.

**color code for carbon resistors**

The colour codes are used to mark its resistance.

Memory tip: B B Roy of Great Britain have Very Good Wife.

Gold : 5% tolerance

Silver : 5% tolerance

No colour: 20% tolerance

**Illustration**

**Drift Velocity**

Drift velocity is defined as the average velocity with which free electrons get drifted in the di¬rection opposite to the direction of the applied electric field.

; where m is the mass of electron, τ is the electric field, x is the relaxation time.

The average time between two successive collisions is called relaxation time.

**Mobility** μ is defined as the ratio of magnitude of the drift velocity to electric field strength.

Electric current In terms of drift velocity

where, n = number density of free electrons

e = electronic charge

a = area of cross section.

V_{d}= drift velocity of electron

j = current density

**Combination of Resistors
1. Series combination**

In series equivalent resistance can be obtained by the formula:

R

_{eq}= R

_{1}+ R

_{2}+ ……… + R

_{n}

- Current in each resistor will be same.
- If V is potential difference across the series combination of resistors and if V
_{1},V_{2},V_{3}…. are the potential diferences across individual resistors, then V = V_{1}+ V_{2}+ V_{3}+….

**2. Parallel Combination**

First end of all resistances are connected to one point and last end of all resistances are connected to the other point.

= + + ………+ R

- Potential difference across each resistor will be same.
- If I
_{1},I_{2}, I_{3}……. are the currents in the re¬sistors, then the total current I drawn by the parallel combination of resisitors willl be:

I = I_{1}+ I_{2}+I_{3}+……..

If n identical resistors each of resistance r are connected in:

- series combination R= nr
- parallel combination R=

**Electromotive Force and Terminal Potential Difference of a Cell**

- emf (E) of a cell is the potential difference between two terminals of the cell when there is no flow of current through it.
- The terminal potential difference (V) of a cell is the potenital difference between two terminals of the cell when current flows through it.

**Internal resistance (r)**

It is the resistance offered by the electrolyte of a cell to the flow of current between its electrodes. It depends on

- separation between electrodes.
- concentration and nature of electrolyte
- area of immersed part of electrodes.

**Relationship between r, R, E and V is**

V < E when current is drawn from the cell. V > E when charging of the cell takes place.

Note: During charging of the cell y = E + Ir.

**Combination of Cells**

- Series combination of n identical cells of emf E and internal resistance r each is equivalent to a total emf of nE and a total internal resistance of nr.
- Parallel combination of n identical cells of emf E and internal resistance of r each, is equivalent to a total emf of E only and total internal resistance of .
- If n cells are connected in series in each row and m such rows are connected in parallel then current drawn through an external resistance R is

- When there are two cells of emf E
_{1}and E_{2}and internal resistance r_{1}and r_{2}respectively, con-nected in parallel the net emf of the combination is:

**Kirchhoff’s Law**

**(i) Junction Rule:** At any junction, the sum of the currents entering the junction is equal to the sum of currents leaving the junction.

**(ii) Loop or Mesh Rule:** The algebraic sum of changes in potential around any closed loop involving resisitors and cells in the loop is zero.

Wheatstone Bridge

In the balanced condition, ie., when no current flows through the galvanometer:

R R

= ; This is the Wheatstone’s Bridge network equation.

**Meter Bridge**

It is an electrical device used to determine the resistance and hence resisitvity of a given wire /conductor.

**Principle:** Wheatsone’s Bridge.

**Theory and Working:** The 1 meter long wire acts as (R+S) of Wheatsone bridge and P(X) and Q(R) fill the left and right gaps respectively. At balanced condition:

where l is the balancing length.

Uses: Metre bridge is used to find the value of unknown resistance, resistivity etc.

Note: A meter bridge is most sensitive when all four resistances and almost equal (balance point at the middle).

**Potentiometer**

Potentiometer is a device used for, measuring potential difference accurately, comparing emfs of two cells and measuring internal resistance of a cell etc.

**Principle:** When a constant current flows through a wire of uniform cross section, the potential drop across any length of the wire is directly proportional to that length.

V ∝ l ⇒ V = kl

**Potential gradient(k):** It is the potential drop per unit length of the potentiometer wire.

**Applications of potentiometer**

Comparison of emfs of two primary cells

Let key a be closed then, E_{1} = kl_{1}

Let key b be closed then, E_{2} = kl_{2}

Note: To get a null point, emf of the driver cell should be greater than the emf of each of the cells being measured. Also the positive terminals of all cells should be connected to end A.

**Internal resistance of a primary cell**

Let K_{1} be closed and K_{2} kept open then we balance the emf of the cell, E = kl_{1}

Let K_{1} and K_{2} be closed then we get the terminal potential difference of the cell V = kl_{2}

= We know r = [ – 1] R

Therefore, internal resistance, r = [ – 1] R

Note: Potentiometer uses null deflection method. At balance point it does not draw any current from the cell and thus measure the ac¬curate emfofthe cell. But a volmeter draws small current and therefore cannot give accurate value ofemf.

**Sensitivity of potentiometer:** It is the measure of ability of the potentiometer to measure very small potential differences and exhibit change in balancing length even for very small change in potential difference.

**Sensitivity of a potentiometer can be increased by:**

- Increasing length of potentiometer wire
- Reducing the current in the circuit using a rheostat.

**Electric Power:** It is the rate at which work is done by source by emf in maintaing an electric current through a circuit.

W = Vlt joules

Electric power, p = = VI = I^{1}R =

**Joule’s Law of Heating:** The electrical energy consumed (or heat produced) in a current car-rying conductor of resistance R in time t is

W = I^{2}Rt = Vlt =

where V is the potential difference across the wire.

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