MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Current Electricity Page 1

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1.

Flow of current in a conductor

• A conductor is a substance which allows electric current to flow through it very easily.
• Metals are good conductors. They contain a large number of free electrons.
• Free electrons move around in a metal randomly when potential difference is not applied across it.
• When a potential difference is applied across a metal, a constant velocity called "drift velocity" is superimposed over the random motion of electrons. There is a net transfer of electrons from one end to another. Hence there is a current in the conductor.
• The drift velocity is given by,
 Vd = j/ne Where Vd = drift velocity j = current density (current/unit area of cross-section) n = number of free electrons per unit volume e = electron charge
• Electric current through a conductor is the rate of flow of charge through a conductor.

 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

• Copper vessel itself serves as anode.
• Vessel contains CuSO4 which acts as depolariser.
• A porous pot containing the electrolyte, dilute sulphuric acid, is placed inside the CuSO4 solution.
• Zn rod is cathode, placed in porous pot.
• e.m.f. = 1.1 V.

Lechlanche Cell

• The positive terminal is a carbon rod and the negative terminal is a zinc rod.
• Electrolyte is a solution of ammonium chloride placed in a glass vessel.
• MnO2 + graphite powder is the depolariser.

Dry Cell

• It is a special form of Lechlanche cell.
• Electrolyte is a paste.
• e.m.f = 1.5 V.

Secondary cells

• These cells are rechargeable.

• Lead peroxide PbO2 is the positive terminal, spongy lead is the negative terminal.
• Dilute sulphuric acid is the electrolyte.
• e.m.f. = 2V when fully charged.

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 = I R V

Unit of conductance : Siemens or mho.

 1 siemens = 1 ampere 1 volt

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

 s = 1 = L r RA

Unit of
s  : Siemens/metre.

4.

Kirchhoff's Laws for steady currents

These laws are used for analysis of electrical networks.

 Kirchhoff's 1st law

Statement : The algebraic sum of the currents passing through any junction or node in an electrical network is zero.
S In = 0

Sign convention

 Currents going towards junction + sign Currents going away from junction - sign

Example

At junction P,
i1
- i2 - i3 - i4 + i5 = 0

 Kirchhoff's 2nd 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 InRn + S En = 0

Sign convention

 p.d. across resistances E.M.F.s. In the direction of current - sign From + to -terminal - sign Opposite to current + sign From - to +terminal + sign

Example

 (1) For loop ABCDEFA, - i1R1 + i3R3 - E2 + E1 = 0 (2) For the loop ABEFA, - i1R1 - i2R2 + E1 = 0 (3) For the loop BCDEB, i3R3 - E2 + i2R2 = 0

5.

Wheatstone's Network

Balanced Network

Unbalanced Network

1.

The current passing through galvanometer
iG = 0

1.

The current passing through galvanometer
iG
¹ 0

2.

B and D are equipotential points.

2.

B and D are not equipotential points.

3.

 P = R Q S

3.

 P ¹ R Q S

4.

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

4.

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

 Meter Bridge: (Modified Wheatstone's Network)

When bridge is balanced,

 R1 = R(AD) R2 R(DC)

 R1 = l1 R2 l2

 Sources of errors
• The wire may not have a uniform cross-section.
• Contact resistance where the wire is joined to copper strips may not be negligible.
• The ends of the wire may not exactly coincide with 0 and 100 marks on the metre scale.
 To minimize the errors
• Null point should be obtained in the middle one-third portion of the wire, i.e. in the range 33 cm to 66 cm.
• Resistances in the left gap and right gap should be interchanged and the experiment should be repeated. The correct value of unknown resistance is then the average of its values in left and right gaps.
 i.e. X = (X) while in left gap + (X) while in right gap 2

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

• Balance point is found instead of null point.
 · G = R lg Where lg = balancing length opposite galvanometer. lR lR = balancing length opposite resistance R.

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