# Electricity - DC current circuit laws.

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Introduction

DC Current Circuit laws:

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

- 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

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 = IR

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.

Middle

Directional

(not proportional)

Resistor networks

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:

- Find the total resistance in the circuit
- Use I=V/R to work out the total current in the circuit
- Divide the total current by the sum of the resistors in that branch
- Multiply the answer by each individual resistance value
- 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)

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/ Є

Electric Power

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

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.

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

Scalar quanitity | Vector Quantity |

Speed Distance Time Energy Power Temperature | Velocity Displacement Force Acceleration Momentum |

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

This student written piece of work is one of many that can be found in our GCSE Electricity and Magnetism section.

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