Lecture 3.10

Electrical safety

Alternating current

ELECTRICITY

Alternating Current (ac) Batteries are a source of steady or direct voltage. Current in a circuit powered by a battery is also steady and is called direct current (dc)

t

V V0 Voltage (& current) are

constant

Direct voltage (current) dc

Nearly all the electricity we use is in the form of alternating current (& voltage) termed ac

Alternating Current (ac):

V

-V0

0 t

+V0

0

-V0 •generally sinusoidal. •current also alternates

Voltage periodic: • Magnitude and direction changes

Alternating Current (ac)

0 sinV V tω=V

-V0

0 t

+V0

0

-V0

2 2 /f Tω π π= =Angular frequency

I

0 t

+I0

0

-I0

0 sinI I tω=

Time averaged value of sine function over one or more cycles is zero

Average values of the current and voltage is zero

R

0 sinV V tω=

0 sinI I tω=

Alternating Current (ac)

-

R

+

V

dc

ac: Average value of the current is zero

However the power consumed in an ac circuit is not zero because dissipation of energy in the resistance does not depend on the direction of the current. ( Power = R I2 > 0 )

I

0 t

+I0

0

-I0

Electrical power consumed by any resistive component in a circuit is P =I2R

0 sinI I tω=

ac

2I20I20

12

I

t 0

( ) ( )220

12ave

I I=

( )2 210 02

12rms aveI I I I= = =

2 2 20 sinI I tω=

rms effI I=

Alternating Current (ac)

always positive 2I

Average value of 2I

Root mean square (rms) value

Similarly ( )012rmsV V=

rms effV V=

Square root of the average value of the square of the current

0 sinI I tω=

Alternating Current (ac)

0 sinI I tω=I

0 t

+I0

0

-I0

Ieff

T

ac voltage and current are always characterized by their effective (or root mean square ) values:

where Vo, and Io are the amplitudes or maximum values of the voltage and the current.

T is the period (= 1/f)

I0 is the maximum current value or current amplitude

Average current value is zero.

and √2 Vo Veff = Ieff =

√2 Io

Alternating Current

An alternating current with a maximum value of 3 amps will produce the same heating effect in a resistance as a direct current of (3/√2)amps

ac mains varies at a rate of 50 times per second– frequency of 50 cycles per second

So periodic time (time for one cycle) T= (1/50)s = 20x10-3 s = 20 millisecs

SI unit of frequency named after German Physicist Heinrich Hertz 1857-1894.

ac mains---frequency 50 Hertz ----50Hz

I

0 t

+I0

0

-I0

Ieff

T

and √2 Vo Veff = Ieff =

√2 Io

Alternating Current I

0 t

+I0

0

-I0

Ieff

T

and √2 Vo Veff = Ieff =

√2 Io

Meters that measure ac current and voltage Calibrated to measure: effective (or rms ) current and voltage Ieff and Veff

ac power Pave = IeffVeff

Power in an ac circuit

since V0=I0R

since I0 = V0/R

( IoVo) 2 Pave =

(Io)2R 2 Pave =

(Vo)2 2R

Pave =

Pave = (I0/√2) (V0/√2)

Power in a dc circuit 2P I R=P IV= 2VPR

=

ESB provides electricity • voltage of 220V •frequency of 50Hz.

The period of the oscillations is: T = 1/50Hz = 0.02s = 20 milliseconds.

220V is the effective or rms value of the voltage: Veff = 220V

amplitude V0 is: V0 = Veff *√2 = 311V

The effective current going through a 100W light bulb is:

Ieff = Pave/Veff = (100/220) A = 0.45A

Alternating Current

Mains voltage swings from +311V to -311V 50 times every second giving an effective voltage of 220V.

Nearly all the electricity we use is in the form of alternating current (& voltage ) termed ac.

Alternating Current

Why?

1. ac voltage (compared with dc voltage) can be increased or decreased easily (with a transformer) 2. High voltage can be transmitted more efficiently

Transmission of electrical energy from generating stations to homes and businesses.

Transmission more efficient at high voltages

Transmission lines (cables) 100’s km long Therefore resistance of cables is significant

energy loss is reduced by reducing current

2ave effP I R=

Alternating Current

Want to deliver a power P to the substation where the transmission line arrives

Power loss in transmission cable of resistance R :

To minimise loss need to increase voltage for a fixed power P to be delivered. Typically 100-700 kV

Step down transformer used to convert the voltage to 220V for use in home or workplace.

2loss effP RI=

2

2loss eff

eff

PP RI RV

= =

Example

A maximum ac voltage of 240 V at a frequency 50 Hz is connected across a 530 Ω resistor. Find (a) rms voltage. (b) rms current. (c) the average power and (d) the maximum power dissipated in the resistor. R

0 sinV V tω=

0 sinI I tω=(a) 0 2rmsV V= ×

0 240 1702 2rms

V VV V= = ≈

(b) 170 0.32530

rmsrms

V VI AR

= = ≈Ω

(c) ( )22 0.32 530 54.3ave rmsP I R A Watts= × = × Ω =

(d) 2 2 2

maxmax

1702 2 109530

rmsV VP WattsR R

= = = =

If the frequency is doubled, does the average power dissipated in the resistor increase, decrease or stay the same.

Electrical Power Example

A 100W bulb operates at a voltage of 220V. Determine the resistance of its filament.

Pave = V2/R or R =V2/Pave

R = (220)2/100 = 484Ω

Determine the rms and peak currents through the bulb

Pave = IrmsVrms

100 0.455220

averms

rms

PI ampsV

= = =

( ) ( )0 2 2 0.455 0.643rmsI I amps amps= = =

250 kV high voltage transmission cable 10km long, resistance 280 Ω supplying 100 MW of power. Bird’s feet are 7 cm apart.

Bird sitting on high voltage transmission cable. Why is it not electrocuted?

Example

Current in the cable P IV=100 400

25P MWattsI ampsV kV

= = =

Resistance of 7 cm length 2

43

7 10 280 19.6 1010 10

mRm

−−×

= × Ω = × Ω×

Voltage between feet 4400 19.6 10 0.784V IR V−= = × × =

Assume resistance through body = 8 kΩ

Current through bird = 60.784 98 108

V ampsk

−= ×Ω

Current through bird = 250 31.258

kV ampsk

=Ω

Electrical safety Hazards: Thermal & Electrical shock

Heat produced faster than it can be dissipated

R3 R2

I2 I3 I4 I5 I6

e.g. As more resistances (appliances) are added in parallel current increases

Thermal

Normally thermal energy produced in wires is negligible unless current becomes very large

Power dissipated in the feed cable P = I2Rw Power proportional to current squared

R1

I1 I

V

Rw

~

~ fuse

Rw represents the resistance of the wires

Electrical safety

Short circuit is also a thermal hazard

Short circuit: insulation breaks down Wires touch >> small contact resistance > large current> heating in wires

P =V2/Rs

Rs is extremely small, hence since V is constant Power is very large>> thermal damage

Prevention –include circuit breaker or fuse. Interrupts current if it exceeds specific value

Heat produced can be large >>>>>ignition of adjacent material>> fire

Prevention –include circuit breaker or fuse. Interrupts current if it exceeds specific value

~ V

appliance

Insulating case

2-pin plug

Ground

live

neutral

Electrical safety Shock Hazard Possibility of current passing through person to earth

Impact on person depends mainly on the current

Maximum harmless current (at 50Hz) ≈ 5mA

Some appliances use an insulated two wire system: Appliance has insulating enclosure to prevent direct contact with current. Insulation has very high electrical resistance

Risk reduction

Electrical safety Shock Hazard

Old appliances sometimes used a two wire system insulated from a metal enclosure

Safe unless insulation breaks down

~ V

appliance

metal case 2-pin plug

Ground

live

neutral

Insulation

Electrical safety Shock Hazard If insulation breaks down and live wire contacts the metal case

Any person touching the case is in parallel with the full voltage

~ V

appliance

metal case 2-pin plug

Ground

live

neutral

Ip = V /Rp Current passing through person =

Severity of shock depends on resistance to ground Rp

Bare feet on wet ground > low resistance> very severe

Shoes on rubber mat > high resistance> little affect

Rp

220V/5mA = 44kΩ

It essentially connects the case of appliance through the plugs and sockets to a copper rod inserted into earth outside house. If the live wire touches the metal case, current will go directly to the earth.

~ V

appliance

Grounded Metal case

ELCB

3 pin plug Ground

live

neutral

ground

Live - brown Neutral – blue Earth – green/yellow

Electrical safety Three wire system Additional Earth line for safety

Earth Leakage Circuit Breaker

Electrical safety

~ V

appliance

Grounded metal case

ELCB

3 pin plug Ground

live

neutral

Safety device makes use of Faraday’s law

Coil magnetically senses any difference in the current in the live and neutral wires and activates circuit breaker >5mA

Current in live and neutral wires should be equal unless short circuit occurs in the applicance e.g to Earth

V in

Circuit breaker

Iron ring

Will a 220V hospital circuit protected by a 15A circuit breaker be able to operate a 200W ECG monitor, a 1200W microwave oven and eight 100W lights simultaneously? Veff = 220V Ieff = 15A

The maximum power consumption allowed is: P = IeffVeff = 220V x15A = 3300W

All the apparatus will consume:

P = 200W + 1200W + 8*100W = 2200W

So all apparatus will be able to operate simultaneously.

Example