Electric Current

Electric Current • An electric current is a flow of charge. • The electric current in a wire is defined as the net amount of charge that passes through it per unit time at any point. • Electric current is • measured in ampere, A. • Where 1 A = 1 C s-1.

Conventional Current • The direction of a Conventional current is the direction along which imaginary positivecharge carriers may be imagined to flow. • In a wire, electrons are the only chargedparticles moving in an electrical current. • At the right, negative • charges moving to the left • is equivalent to positive • charges moving to the • right.

Microscopic view of Electric Current • In a conducting wire, the free electrons are moving about randomly at high speeds, (about 1/1000 of the speed of light) bouncing off the atoms. • Normally, the net flow of charge is zero.

The Mechanism of current flow (1) • When an electric field exists in the wire, the electrons feel a force and begin to accelerate and gain kinetic energy. • On colliding inelastically with lattice ions,the motion is repeated very rapidly at short time intervals. • The electrons soon reach a steady speed known as their drift speed. • The macroscopic effect is a steady current flow.

The Mechanism of current flow (2) • Microscopically electric field energy is converted initially to the mechanical kinetic energy of the drifting electrons, and then to the kinetic energy and potential energy of the vibrating lattice ions. • Macroscopically the internal energy of the metal increases resulting in a temperature rise.

v Drift Speed (1) • The diagram below shows part of a wire of cross-sectional areaA. • The current in the wire is I. • There are n free electrons per m3 of the wire. • The charge on each electron is e. • The electrons move with a drift speed of v. • It can be shown that I = nAve

Drift Speed (2) • The drift speed is normally (~10-4 m s-1) very much smaller than the electrons average random speed (~106 m s-1). • For example, the drift speed through a copper wire of cross-sectional area 3.00 x 10-6 m2, with a current of 10 A will be approximately 2.5 x 10-4 m/s.

Free Electron Number Density • The table below shows some typical values forn.

Speed of Electric Signal • The speed of the electric signal is the speed of light. This means that, at the speed of light, the removal of one electron from one end of a long wire would affect electrons elsewhere. • If you think of a copper wire as a pipe completely filled with water, then forcing a drop of water in one end will result in a drop at the other end being pushed out very quickly. This is analogous to initiating an electric field in a conductor.

Electromotive Force (e.m.f.) • The e.m.f. of an electric source is defined as the energy (chemical, mechanical or light, etc.) converted into electrical energy when unit charge passes through it. • Unit : volts (V) • The e.m.f. equals the potential difference across the terminals of an electric source on open circuit.

Potential Difference • The potential difference across two points in a circuit is defined as the energy converted from electrical energy to other forms of energy per unit charge passing between the points outside the source. • V = IR

 r Internal Resistance • The resistance within a source of electric current such as a cell or generator is called the internal resistance. • Some of the electrical energy is wasted due to the heating effect inside the cell. • A real cell can be modelled as it had a perfect emf  in series with a resistor r as shown.

V V A I Measurement of Internal Resistance • The circuit below shows an experiment to measure the emf and internal resistance of a cell.  Slope = - r

Po 0 R Variation of power output with external resistance Power output to R is a maximum when R = r, internal resistance. Pmax r

 0 R Variation of efficiency with the external resistance The efficiency equals 50 % when R = r 100 % 50 % r

Examples of Loads in an Electric Circuit (1) • Loading for greatest power output is common in communication engineering. • For example, the last transistor in a receiver delivers electrical power to the loudspeaker, which speaker converts into mechanical power as sound waves. • To get the loudest sound, the speaker resistance (or impedance) is matched to the internal resistance (or impedance) of the transistor, so that maximum power is delivered to the speaker.

Examples of Loads in an Electric Circuit (2) • The loading on a dynamo or battery is generally adjusted for high efficiency. • If a large dynamo were used with a load not much greater than its internal resistance, the current would be so large that the heat generated would ruin the machine. • With batteries and dynamos, the load resistance is made many times greater than the internal resistance.

Resistance in a Conductor (1) • Notice that the electrons seem to be moving at the same speed in each one but there are many more electrons in the larger wire. • This results in a larger current which leads us to say that the resistance is less in a wire with a larger cross sectional area. It can be shown that R1/A.

Resistance in a Conductor (2) • The length of a conductor is similar to the length of a hallway. A shorter hallway would allow people to move through at a higher rate than a longer one. • So a shorter conductor would allow electrons to move through at a higher rate than a longer one too. • It can be shown that R  l.

Resistivity of a material  is called the resistivity of the material. The unit of  is m.

Resistivities of various materials

Effect of temperature on the resistance of a metal conductor (1) • Heat on the atomic or molecular scale is a direct representation of the vibration of the atoms or molecules. Higher temperature means more vibrations. • When the wire is cold the protons are not vibrating much so the electrons can run between them fairly rapidly.

Effect of temperature on the resistance of a metal conductor (2) • As the conductor heats up, the protons start vibrating and moving slightly out of position. As their motion becomes more erratic they are more likely to get in the way and disrupt the flow of the electrons. As a result, the higher the temperature, the higher the resistance.

I I V V 0 0 The variation of Current with applied potential difference (1) • Filament lamp • Ohmic conductor

I I V V 0 0 The variation of Current with applied potential difference (2) • Thermionic diode • Thermistor

I I V V 0 0 The variation of Current with applied potential difference (3) • Gases • Electrolyte

I V 0 The variation of Current with applied potential difference (4) • Semiconductor diode

Q P Slide-wire potentiometer • The potentiometer consists of a long wire placed on a metre rule. A fixed potential difference is maintained across this wire by a cell E called the driver cell. • A sliding contact is used to apply a fraction of this potential difference across another wire PQ, connected in parallel across AJ. The p.d. in this wire is then known to be equal to the p.d. across the part AJ of the potentiometer wire.

Rotary Potentiometer • By rotating the wiper to touch the different places on the horse-shoe, we can 'tap-off' any fraction of the input voltage we want from zero up to the full size of the input.

Multimeters • A multimeter is a moving-coil galvanometer adapted to measure current, p.d. and resistance. • A rotary switch allows the various ranges to be chosen.

Connections in a Multimeter (1) • For measuring current ranges, some internal resistors in parallel formed a shunt across the meter. • For measuring p.d. ranges, more internal resistors in series formed a multiplier in series with the meter.

Connections in a Multimeter (2) • For measuring resistance, an internal battery and rheostat are connected in series with the meter and the unknown resistance. • To measure resistance the terminals are short-circuited and the rheostat adjusted until the pointer gives a full deflection, i.e. is on the zero of the ohms scale. • The zero resistance reading will correspond to the maximum current value.

Electric Current