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Electricity DC Circuits

The Mechanism Of Conduction In Metals

The structure of metals is such that each atom ( on average ) has one outer electron which is not used in chemical bonding. When no current is flowing these free electrons move randomly throughout the structure ( v = 106 ms-1 ). When a potential difference is applied, an electric field is produced. The free electrons in the field are urged to move in opposite direction to the field. There is a net flow of charge. Good conductors of heat are good conductors of electricity.

Electric Current

• It is the flow of charged particles ( electrons in metals ) OR

• It is the rate of flow of charge through a conductor ( i.e.: the amount of charge passing a certain point ).

I = Q/t            Ampere (A) = Coulomb (C)/Second (s)

For A Current To Flow:

• A potential different should be present between the 2 terminals of the circuit.

• The circuit should be closed ( a closed conducting path ).

Measuring The Current ( Ammeter )

Many meters are based on the turning effect of the magnetic field on a current-carrying coil.

• Galvanometer:- Is a device to detect small currents.

• Milliammeters:- Is a galvanometer calibrated to measure small currents.

When a current passes through the coil, a magnetic field is produced which makes the coil to act like a piece of magnet. The magnetic field due to the two surrounding poles causes the coil to rotate. The larger the current passing through the coil, the greater the deflection is.

The coil comes to rest when the couple turning is balanced by an opposing couple caused by two springs. The ammeter is connected in series in any electric circuit. It has very low resistance.

Electromotive Force ( e.m.f )

A chemical reaction inside the cell causes accumulation of the +ve charges on one end ( or pole ) and of -ve charges on the other end. This creates a potential difference. Energy flows from higher to lower potential.

Batteries push out charges in the form of electrons when a chemical reaction takes place inside them. For this to take place, a conducting path must be found between the two poles of the battery. As they flow, potential energy lost by the electrons is converted into heat, light energy ..... etc.

Definition of the e.m.f:- It is the potential difference across the terminals of a cell when it is not supplying a current, i.e.: in an open circuit.

It's measured by connecting a voltmeter across the two terminals of the battery ( i.e.: in parallel ). When a cell supplies current, the potential difference across its terminals drops because it has an internal resistance r.

Ohm's Law & Resistance

When electrons are pushed through a conductor, they collide with its atoms. The presence of atoms resists the motion of the electrons. As a result, the electrons lose energy and heat is given off.

Ohm's Law:- The current flowing through a conductor is directly proportional to the potential difference across the ends providing that the temperature ( and other physical conditions ) remains constant.

• V α I

• V = IR

• Ohm () = volt/ampere

We can have approximately Ohmic resistance when we have small currents.

A conductor has a resistance of 1 when a current of 1 A flows through it when a potential difference of 1 V is applied across it.

R α l            R α 1/A            R = (ρ l)/A

• l = length of the conductor

• A = cross sectional area of the conductor = π r2 ( when a wire is considered )

• ρ = resistivity of the material from which the conductor is made.

ρ = (RA)/l        m

It is the resistance of a conductor of unit length and unit cross-sectional area.

• Ohmic resistors:- Are those obeying Ohm's Law

• Non-Ohmic resistors:- Are those for which the value of the resistance vary with the current. They do not give a direct proportionality between V α I.

Resistance of most metals increase with temperature. Electric conductivity = σ = 1/ρ  -1m-1

The resistance at a temperature (T) = RT = R0 [ 1 + α ( T - T0 ) ], where R0 is the resistance at a reference temperature T0 & α = temperature coefficient of the resistance/ 0c-1 .

This applies to resistivity ρT = ρ0 [ 1 + α ( T - T0 ) ].

Resistance In Series

• I is the same

• V = I R = I ( R1 + R2 + R3 )

• i.e.: R =  R1 + R2 + R3, R is greater than any individual resistance.

• V = V1 + V2 + V3

R is the equivalent resistance ( or combined resistance ) which can replace all the resistances without affecting the value of the current I.

Resistance In Parallel

• V is the same

• I = I1 + I2 + 13

• V/R = V/R1 + V/R2 + V/R3

• 1/R = 1/R1 + 1/R2 + 1/R3

• R is less than any of the resistances. If any of the branches is open-circuited the others will not be affected, but the current will be distributed.