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1.

Flow of current in a conductor

V_{d} =

^{j}/_{ne}

Where V_{d} =

drift velocity

j =

current density (current/unit area of cross-section)

n =

number of free electrons per unit volume

e =

electron charge

I = ^{q}/_{t}

1 ampere = 1 coulomb/1 second.

2.

Sources of E.M.F.

E.M.F.: The work done (or the energy supplied) by a source in taking a unit positive charge around a closed circuit is called the electromotive force (e.m.f.) of the source.

Types of cells:

1. Primary cells

2. Secondary cells.

Primary cells: When chemicals in these cells are used up, they have to be replaced. These cells cannot be recharged. Example: Simple Voltaic cell, Daniel cell, Lechlanche cell, Dry cell. Simple Voltaic Cell: In this cell, Cu is the positive electrode; Zn is the negative electrode; dilute sulphuric acid is the electrolyte. e.m.f. = 1.08 V.

Defects: (i) Local action: Impurities in Zn rod form a number of tiny cells on the surface of the rod. Hence there is a consumption of Zn rod even when the cell is not being used. To prevent this, Zn rod is coated with mercury. (ii) Polarisation: It is caused by deposition of hydrogen on the copper rod. The hydrogen layer acts as bad conductor, increases internal resistance and sets up back e.m.f.

Daniel Cell

Lechlanche Cell

Dry Cell

Secondary cells

Lead accumulator

3.

Electric Current - Ohm's Law

The current I in a metallic conductor is directly proportional to the potential difference applied across it so long as the physical conditions of the conductor remain constant.

V

= R

I

Unit of R : ohm Symbol : W Definition of 1 ohm : A conductor has a resistance of 1 ohm when a potential difference of 1 volt across it causes a current of 1 ampere to flow through it.

1 ohm =

1 volt

1 ampere

Specific resistance : The specific resistance of a material of a conductor is the resistance offered by a unit cube of the conductor when the current flows parallel to its edges. It is also known as resistivity.

r =

RA

L

OR It is the resistance of the conductor whose area of cross-section is 1 sq. unit and length is 1 unit. Unit of r : ohm-metre (Wm). Conductance : The reciprocal of resistance is called conductance. It is denoted by G.

G =

1

=

R

Unit of conductance : Siemens or mho.

1 siemens =

Conductivity : The reciprocal of resistivity (specific resistance) is known as conductivity (or specific conductance). It is denoted by s.

s =

r

Unit of s : Siemens/metre.

4.

Kirchhoff's Laws for steady currents

These laws are used for analysis of electrical networks.

Kirchhoff's 1^{st} law

Statement : The algebraic sum of the currents passing through any junction or node in an electrical network is zero. S I_{n} = 0 Sign convention

Currents going towards junction

+ sign

Currents going away from junction

- sign

Example

At junction P, i_{1} - i_{2} - i_{3} - i_{4} + i_{5} = 0

Kirchhoff's 2^{nd} law

Statement : In a closed loop of an electrical network, the algebraic sum of the potential differences across all the elements and the e.m.f.s applied is zero. S I_{n}R_{n} + S E_{n} = 0 Sign convention

p.d. across resistances

E.M.F.s.

In the direction of current

From + to -terminal

Opposite to current

From - to +terminal

(1)

For loop ABCDEFA, - i_{1}R_{1} + i_{3}R_{3} - E_{2} + E_{1} = 0

(2)

For the loop ABEFA, - i_{1}R_{1} - i_{2}R_{2} + E_{1} = 0

(3)

For the loop BCDEB, i_{3}R_{3} - E_{2} + i_{2}R_{2} = 0

5.

Wheatstone's Network

Balanced Network

Unbalanced Network

The current passing through galvanometer i_{G} = 0

The current passing through galvanometer i_{G} ¹ 0

B and D are equipotential points.

B and D are not equipotential points.

P

Q

S

¹

Currents through P and Q same. Currents through R and S same.

Currents through P and Q different. Currents through R and S different.

Meter Bridge: (Modified Wheatstone's Network)

When bridge is balanced,

R_{1}

R(AD)

R_{2}

R(DC)

l_{1}

l_{2}

Sources of errors

To minimize the errors

i.e. X =

(X) while in left gap + (X) while in right gap

2

Kelvin's Method (to find the resistance of galvanometer)

· G = R

l_{g}

Where lg =

balancing length opposite galvanometer.

l_{R}

l_{R} =

balancing length opposite resistance R.