electricity notes

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Current, I (amps, a)

current = charge, Q/ time, t

The current is the rate at which charge passes a point. It is measured in series with an ammeter.

In DC circuits the current always flows directly around from the positive terminal to the negative terminal.

inside a conductor ( like the wire completing a circuit) an electric field is formed, the direction of the electric field is the same as the direction of the force on a positive charge. Both positive and negative charges experience a force, but in a solid, the electrons which are free to move (the more conductive a solid is the more electrons can move freely) drift towards the positive terminal, this flow of electrons is an electric current.

the electric charge of the electric current has the symbol Q and the unit coulomb, C.

series circuit

the current will have the same value in each part of the circuit

parallel circuit

the current adds up to the current from the supply I= I1+!2...

Kirchhoff's Current law

Junction rule- the sum of currents entering a junction equals the sum of currents leaving it. total I out= total I in

method-

choose and label the direction of the currents

form equations for each junction

Explanation- Explain why the current is moving against a battery ( as a result of Kirchhoff's current law)

state the law (giving a mathematical explanation)

(general explanation) when the positive terminal of another battery at a higher potential (voltage) than the first battery ( voltages of which depend on the circuit). Current always flows from higher potential to lower potential

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Voltage, V (volts, V)

Voltage = change in energy, E / charge moved, q

The voltage is a measure of the work done or the change in energy on each coulomb of charge as it moves between two points. It is measured in parallel to the circuit component using a voltmeter.

the voltage V = IR only changes when there is a change in the current or resistance of the circuit.

series circuit

the voltage adds up to the supply V=V1+V2...

parallel circuit

the voltage is the same across all branches in parallel

Batteries in series

Add battery voltages together

batteries push from the positive terminal when the two batteries in series are pushing the current in opposite ways the voltages will cancel.

Kirchhoff's Voltage law

Loop rule- The sum of the potential differences (positive and negative) around the closed path (loop) in a circuit must be zero. -V1+V2+V3=0

Method-

Put an arrow against each component in the circuit pointing to the 'high energy' side of the component.

Chose the direction to go around the loop, if you go 'with' the arrow through a component, its potential difference is added, if you go 'against' the arrow the components potential difference is subtracted

create an equation for each loop

once voltages have been calculated for a resistor using the voltage law V=IR can be used to calculate the current through these components

this can then also be used with the current law to calculate the current where the circuit branches (junctions). when there are multiple unknowns these can be solved simultaneously with the equations created from both laws.

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Resistance R, (ohms or volts per amp)

resistance = voltage / current

The resistance limits the flow of current through a conductor when it is connected to a voltage supply.

Series circuit

the resistance of the whole circuit is given by

R = R1+R2...

parallel circuit

the resistance of the whole circuit is given by

1/R= 1/R1+ 1/R2...

Internal resistance, r

The internal resistance is the resistance inside a voltage source, caused by the chemicals inside a battery of components inside a power supply having a resistance that also affects the current. Can be calculated by short-circuiting a battery.

EMF and internal resistance

the potential difference across the terminals of a voltage source, where no current is flowing from t, is called the EMF. If a circuit is connected so that the current flows from the source, the voltage across the terminals will be less than EMF.

V= (EMF) - Ir

change in internal resistance

when the internal resistance increases (as it is in series) the total resistance of the circuit increases. The pushing voltage EMF has remained the same.

V=IR, therefore, the current (I) must have decreased.

Therefore the lamp for which the R will remain unchanged, and the voltage will decrease resulting in the lamp becoming dimmer.

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Power, p (watt, w)

The power is the rate at which energy is transformed

power = current * voltage (resistance can be substituted into this formula using V= IR or I=V/R)

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Capacitors

A capacitator is a component which can store charge. They are made up of two parallel metal plates separated by an insulator (dielectric).

The capacitor plate closest to the negative terminal of the power supply is 'stacked' with electrons (negative charge), causing the opposite plate to become positively charged (plates have an equal and opposite charges)

there is no movement of charge between the plates s they are insulated by the dielectric.

When fully charged the flow of electrons stop, the potential difference is equal to the supply voltage, and an electric field exists between the plates E=V/d

Capacitance, c (Farad, F)

Capacitance = charge, Q/voltage

the capacitance is the amount of charge a capacitor can store when connected across a potential difference of 1Volt

capacitance is affected by

the area of the plates ( when increased the capacitance is also increased)

the distance separating the plates (when increased the capacitance is decreased)

the properties of the dielectric. (when a dielectric is placed between the plates the capacitance creases.)

The dielectric constant, (EMF)r- gives the proportion by which the capacitance will increase, this is called the dielectric effect.

(EMF)r = C dielectric/C air as it is a ratio between the Cd and Ca it has no units.

(EMF)o = 8.84 *10^-12 Fm-1 the constant of the absolute permittivity of free space, when there is air or a vacuum between the plates.

therefore C= (EMF)r(EMF)o A/d

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Networks of Capacitors

series circuit

The charge on each capacitor is the same

The voltage across each capacitor add to give the supply voltage

The combined capacitance is given as a result of C=Q/V

1/Cs=1/C1 +1/C2...

parallel circuit

the charge on each capacitor add to give the sum of the charge stored

the voltage across each capacitor is the same as the voltage of the power supply.

the combined capacitance is given as a result of C=Q/V

Cp = C1 + C2...

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Energy in a Capacitator

Energy produced by a cell

potential Energy=charge * Voltage

Energy stored in a Capacitator

potential Energy= (charge*voltage)/2

the resistance of components transfer 1/2 energy to heat energy

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Charging and discharging Capacitors

Charging

As a capacitor charges:

the Voltage increases to the supply voltage and the current decreases as the plates become 'full' of charge.

once fully charged the flow of electrons stops, both plates will have equal and opposite charge, an electric field exists between the plates and the potential difference is equal to the supply voltage.

Discharging

As the capacitator discharges:

the voltage across the plates decreases as the charge 'leaves' the plates the current decreases.

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Resistor and Capacitor in series

Vs = V resistor + V capacitor

when the voltage of the resistor decreases the voltage of the capacitor will increase

the higher the resistance the slower the charging or discharging

the resistance, therefore, affects the time constant

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time constant

the time constant is a measure of the time taken to charge or discharge a capacitator. It depends on the resistance of the circuit (how much the circuit flows) and the capacitance of the capacitor (how much charge can be stored).

This is the time taken in seconds for the capacitor to charge by 63.5% or to discharge by 7.5% of the total voltage.

t=RC

5time constants =99% charged or fully charged

5 time constants=1% discharged or fully discharged

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Inductors

Electromagnetic induction involves a changing magnetic field in or near a coil or circuit. An induced voltage is produced which can cause a current if the circuit is complete.

When we have current flowing through a wire it has a circular magnetic field around it

the right-hand grip rule- shows the relationship between the direction of current and the magnetic field

this applies to a coil where the direction of current changes as it goes around the coil changing the direction from clockwise to anti-clockwise as it goes around the coil.

When there is a coil of wire (solenoid) a big magnetic field goes through the center of the coils

A magnet moving in and out of a solenoid will induce a current

right-hand grip rule shows the direction of current

When a loop is moved through a magnetic field a current is induced.

However, once the complete loop is in the magnetic field the induced current cancels out (due to direction)

right-hand slap rule can be used to find the direction of induced current through each length of the loop

induced voltage = Magnetic field strength*velocity*Length of wire in the field V = BvL

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Lenz's Law

The Law of conservation of energy states that 'energy cannot be created but can only be changed from one form to another'. so the energy produced by electromagnetic induction must have been supplied to the system in some other form.

Lenz's law states that ' an induced current causes a force to oppose the change which produced it'. so an electric current induced by a changing magnetic field always opposes the force that induced it.

solenoid

This causes a coil to create an opposite pole to repel a magnet that is being moved towards its end and the coil creates a like pole to attract a magnet that is being moved away from its end.

loop in a magnetic field

This causes the induced current to create a magnetic field that produces a force opposite the motion

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Inductance, L (Henrys, H)

The inductance is a measure of a conductors ability to induce a current.

The inductance is increased when an iron rod is placed inside of an inductor as it increases the magnetic field strength, B, and therefore increases the inductance.

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Flux

Magnetic flux is a measurement of the total magnetic field which passes through a given area.

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EMF

In electromagnetic induction, emf can be defined around a closed loop of a conductor as the electromagnetic work that would be done on an electric charge (an electron in this instance) if it travels once around the loop.

(EMF) = -inductance*change in current/change in time

change in current > change in magnetic field > opposing voltage > opposing current > opposing magnetic feild

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Energy in an Inductor

Energy = 1/2*Inductance*Current^2

E =1/2LI^2

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Inductors (mutual inductance)

The transformer

consists of a primary coil (connected to an alternating current supply) and a secondary coil (connected to an output) wound around an iron core.

the changing current in the circuit creates a changing magnetic flux in the iron core. The changing flux passes through the secondary coil, where it induces an alternating voltage.

the voltage in the primary Vp and secondary Vs coils are related to the number of turns in the primary Np and secondary Ns coils.

Step-up transformer (increasing voltage) Vp<Vs, Np<Ns

Isolating transformer (to protect against electric shocks) Vp=Vs, Np=Ns

Step-down transformer (decreasing voltage) Vp>Vs, Np>Ns

In an ideal transformer, the voltage and number of turns are related by Vs/Vp= Ns/Np

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Efficiency of a transformer

The efficiency is the percentage of the input energy which is available as output energy

efficiency =output Energy/ input Energy*100/1

energy loss is reduced by:

using an iron core to ensure a strong magnetic field between the primary and secondary coils

Reducing eddy currents (induced currents in the core), which transform energy to heat energy and can be reduced by making the core from many flat electrically insulated sheet or laminations, rather than just solid iron.

using low-resistance copper wire for the coils

power input=power output since P=VI

VpIp =VsIs

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Inductors (self inductance)

self-inductance

When a coil connected to a power supply in a circuit with a closed switch, it will take time for the current to build up from zero to its steady value. While current is increasing there will be changing magnetic flux in the coil, causing an induced voltage. The applied voltage that already exists across the coil does not affect the induction of this voltage.

an inductor is a device which produces a voltage when the current (and so the flux) changes.

opposing voltage

when the switch is opened the current (flowing from the positive terminal to the negative terminal) is small. this is a result of the change in flux of the inductor when the switch is first turned on, creating an induced voltage which opposes the current that created it. Because of resistance in the circuit, the (emf) decreases over time until it no longer opposes the current allowing the current to increase over time until it reaches its full amount.

Time constant = inductance/resistance

torque = L/R

the time constant is the time for a 63% change in the voltage

Whenever something is changed in the circuit the inductor will try to oppose that change (like in Lenz's law) therefore this applies when the circuit is turned on or off

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AC Circuits

AC: alternating current

instead of current flowing directly around the circuit, each piece of charge alternates backward and forward.

The current is therefore constantly changing at all parts in the circuit.

the charge comes for a supply rather than a battery.

the supply has a supply voltage and a current of the supply.

Voltage alternates and so travels in a sin wave.

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Voltage in AC circuits

Vmax is the peak voltage which is the highest voltage we might get

RMS voltage is the same voltage as what a DC circuit would have if the whole sin graph was averaged out. The power is the same as for a DC circuit at this voltage. (root mean square)

RMS=Vmax/(2)^1/2

Vmax= 2^1/2.VRMS

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current in an AC circuit

The current is also changing in the same way as voltage. so there is again a peak current and an RMS current.

the RMS is an average that gives the same current as a DC circuit at the same power

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frequency and angular frequency

due to oscillation, the voltage has a frequency.

f=1/T

There is also an angular frequency w (rad/s)

w= 2pief

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Capacitors in AC circuits

When current is at its max there will be no voltage built up on the plates. as soon as the current changes and begins to move through the circuit the charge builds up the voltage on the plates. once the charge has built up on the plates and the voltage of the capacitator = the supply voltage the current is opposed by this and so there will be no current in the circuit. the opposite of this occurs when it discharges.

the capacitator voltage is a 1/4 or 90' of a cycle behind the supply voltage.

reactance

capacitator has reactance, Xc (ohms) it is the effective resistance of a capacitator.

Xc=1/wC

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Inductors in AC circuits

when the current starts oscillating for equaling zero there will be a maximum opposing voltage from an inductor. over time as the current builds up the opposing voltage of the inductor will decrease until the current reaches its max this will happen repeatedly as inductors all ways oppose change.

the inductor voltage is a 1/4 r 90' ahead of the supply voltage.

reactance

the inductor will have a reactance, Xl (ohms) which is the effective resistance of the inductor

Xl=wL

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phasor diagrams

always go around anti-clockwise

Phasors can be used to make a triangle where the sides can be solved for using Pythagoras/trigonometry

the angle can be used to calculate the phase

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impedance, Z

The impedance is the total of resistance and the reactance of the capacitors/inductors of an AC circuit.

resonance

when the capacitator reactance and inductor reactance cancel (n the phasor diagram) there is no reactance and so the resistance equals the impedance and the circuit is said to be at resonance.

conditions of resonance- Resistance equals the impedance Xc=XL

effect- minimum impedance, so maximum current

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