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Electricity - DC current circuit laws.

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Introduction

image00.png

DC Current Circuit laws:

image01.png

Charge transfer:

Current is the transfer of charge by charge carriers e.g. electrons, ions or ‘holes’

Charge = Current x Time        ΔQ (charge transferred) Δt (time period) ΔQ      I            image12.png

  • 1C is the charge transferred when a current of 1A flows for one second.
  • 1.6 x 10-19 C is the charge on one electron
  • No. electrons per second = Current / charge per electron

image19.png

I=nAvq (n=number/volume of electrons, q=charge on carriers v=average drift velocity A=cross-sectional area)

In a time, t, the average distance travelled = vt

The average volume the elactrons have moved through = vt

Number of electrons in this volume = nAvt

The charge moving through in t seconds = nAvtq

The charge moving through in 1 second = nAvq = I

Ohmic Conductors:

V = IRimage30.png

Ohm’s law – V s directly proportional to I providing t is constant

Steeper gradient = More resistance, greater V for same I

Gradient= Resistance

1Ω is the R of a conductor that requires a V of 1V for 1A to flow through it

Free electrons move through a wire colliding with atomic centres. This results in electron movement being random. When a pd is applies, a net movement is super imposed on this random movement.image36.png

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Middle

Directional

(not proportional)


Resistor networks

image11.pngimage10.pngimage09.png

image13.png

Parallel resistance

When a parallel branch is added to the circuit, the current can flow through this new branch. The current in common parts of the circuit is therefore greater. The effective resistance between two common points is reduced as greater current is flowing. The effective resistance of a parallel network is less than the resistance of any of the individual resistors.

The current in a branch can be worked out using ratios:

  1. Find the total resistance in the circuit
  2. Use I=V/R to work out the total current in the circuit
  3. Divide the total current by the sum of the resistors in that branch
  4. Multiply the answer by each individual resistance value
  5. Match up the largest resistor to the largest current and so on

Resistance of a wire

R      1/A      1/r2      l       Є (l/A)image12.pngimage12.pngimage14.pngimage15.pngimage12.pngimage12.png

Є = (RA)/l

When Є=R, A/l = 1

The resitivity, Є, of a material is the resistance of 1m3 of that material, its is measured in Ώm’

       = conductivity = 1/ Єimage16.png

Electric Power

The heating of a conductor depends on the electric current through the conductor and the voltage across it.

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Conclusion

Temperature and light sensors can be used in potential dividor circuits. The voltage across them then changes with changing conditions which can be used to activate another circuit. The sensitivity of the circuit ca be changed by using a variable resistor in place of the second resistor.


image28.png

Information is very important in our society and getting data is essential not just to Science but also to buisinesses and industry. Computers and sensors are useful  to collect information automatically and remotely, this is useful in:

  • Hostile environments – nuclear reactor, volcano, deep-sea bed, nuclear reactors, surface of Venus
  • Small confined spaces – air ducts, cells, inside the body
  • Over large areas – counting amount of grass!
  • Cheaper – less manpower & faster
  • Longer and shorter periods of time – Automated industrial plant
  • Accuracy?

The amount of data often has to be cut down, this is done by only keeping abnormal data or by sampling.

Analogue and Digital signals


image29.png

Scalar quanitityimage31.png

Vector Quantity

Speedimage32.pngimage32.png

Distance

Time

Energy

Power

Temperature

Velocity

Displacement

Force

Acceleration

Momentum


image33.png

Reliability

Checking reliability requires repeated measurements. Range = x max – x min The uncertainty in the next measurement being within that range depends on the number of readings:

Uncertainty Δx = ( x max – x min ) / no. of readings

%Δx = ( Δx / x ave ) x 100%

Multiply / divide values = add %Δx

Raising value to a power = power x %Δx

Linear Graphs

image35.pngimage34.png

...read more.

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