Current electricity -A-level physics

Current I

This is the flow of charge

I =  δQ/δt

The S.I. unit of current is Ampere (A)

An Ampere is the current flowing in a circuit when a charge of one coulomb passes any point through the circuit in one second.

Mechanism of conduction in metals (heat effect on metals)

Conduction in metals is due to free electrons. Free electrons have thermal energy, and move randomly through metal from one atom to another. When a battery is connected across the ends of the metal, an electric field is set up.  The electrons are accelerated by the field; they gain velocity and kinetic energy. When they collide with an atom vibrating about its fixed mean position (called a lattice site) they give up some of their energy to it.  Kinetic energy lost is transferred into heat energy within the metal and causes the temperature of the metal to increase.

Although the movement of electron is erratic, on average the electrons drifts in a direction of a field with mean average speed depending on the strength of the field. It is this electron which constitutes an electric current.

The electrical resistance is caused by  the obstruction due to atoms to electron movements.

 

Derivation of I = nAve and J = nve

Consider a section of a metallic conductor in which a current is flowing.

Let I = current through the conductor (A)

L = length of the conductor (m)

A = cross-section area (m²)

n = number of free electrons per unit volume (n)

e = charge on each electron (C)

v = average (drift) velocity of the electron (ms^-1)

 

It follows that

Volume of the section = LA

Number of free electrons in the section = nLA

Total quantity of charge which is free to move = nLAe

Time taken for an electron to travel through the section = L/V

Rate of flow of charge =(nLAe)/(L/v)  = nLAve

Hence current, I = nLAve

Current density,  = (I/A)  = (nLAve)/A  = nLve

 

Potential difference (P.d.)

This is work done in transferring a charge of 1 coulomb from one point to another in a circuit. Whenever current flows from one point to another, it does so because the electrical potential at two points are different. If two points are at the same potential, no current can flow between them.

Resistance (R)

This is the opposition to the flow of current in the material.

Resistance R = (V/I) . The S.I. units of resistance is ohms (Ω)

An ohm is a resistance of a conductor through which a current of one Ampere is flowing when the potential difference across is one volt. i.e. 1Ω = 1VA^-1.

Resistivity (ρ, rho)

Resistivity is electrical resistance across opposite faces of a cube of 1m long

RR = ρ(L/A)   and ρ = R(A/L)  Ωm

Conductivity (λ)

It is the reciprocal of resistivity

λ =  (1/ρ) Ω^-1m^-1

Some conductors have resistances which depend on current flowing through them; but in most cases the resistance of many conductors (metals) depend only on their physical circumstances e.g. temperature. This was discovered by Ohm and such conductors are called ohmic conductors and obey Ohm’s law.

Coulomb

Is the quantity of charge passing in one second through a given cross-section area of a conductor when current flowing is one Ampere.

Electromotive force (e.m.f)

This is the work done in transferring one coulomb of charge around a circuit in which a battery is connected. E.m.f is denoted by E.

 

Ohm’s law

States that the current flowing through a conductor is directly proportional to the P.d. across it provided that there is no change in physical conditions such as temperature of the conductor.

i.e. I = RV

Experiment to determine Ohm’s law

 

The switch is closed the current (I) from ammeter and P.d. (V) from the potentiometer are recorded.

The rheostat is adjusted to obtain several values of I and V

The graph of V against I is plotted.

A straight line graph through the origin implies that V is directly proportional to I

From the graph R =  = tan θ

Factors affecting resistance

1. Length: Resistance increases with the length of a conductor; electron make more frequent collision with atoms when the length of the conductor increases. This reduces drift velocity of free electron hence resistance increases.
2. Cross sectional area (A): Resistance reduces with increase in cross sectional area. When the cross-sectional area increases, the number of electrons that drift along the conductor increases. This implies that there is an increase in the number of electrons per second that pass a given point, thus an increase in current and consequently a decrease in resistance.
3. Temperature: Resistance increases with temperature increase. Increase in temperature causes atoms to vibrate with greater amplitude and frequency about their mean positions. The velocity of electrons also increases making more collision between electrons and atoms. This increase in collision between electron and atoms reduces the drift velocity of electrons and increases resistance.

Ohmic conductors

These are conductors that obey ohm’s law.

Non-ohmic conductors

Are conductors that do not obey ohm’s law; examples

Resistance in combination

resistors in parallel and resistors in series

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Current electricity

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