Electromagnetic transmission summary

The following texts are the property of their respective authors and we thank them for giving us the opportunity to share for free to students, teachers and users of the Web their texts will used only for illustrative educational and scientific purposes only.

All the information in our site are given for nonprofit educational purposes

The information of medicine and health contained in the site are of a general nature and purpose which is purely informative and for this reason may not replace in any case, the council of a doctor or a qualified entity legally to the profession.

Electromagnetic transmission summary

Electric Power Transmission

Power: P= E/t

Power is a measure of the rate of transfer (transmission) or transformation of energy: P = E/t . Transfer (transmission) occurs when energy of one kind is moved from one object/place to another. Transformation occurs when energy of one kind is changed into another kind of energy. Power is measured in Watts, ‘W’, and is equal to one Joule per Second, ‘Js^-1’.

Electric Power: P= IV = q/t * E/q = E/t

Electrical power is transmitted when a voltage, ‘V’, across a component results in a current, ‘I’, through that component. This is because the voltage is a measure of the electrical energy, ‘E’, transferred or transformed by each unit of charge, ‘q’, and the current is a measure of the rate of transfer of unit charges: ‘q/t’.

Electrical Dissipation (Transmission Losses):V= IR

In ohmic devices, such as conductors, the current through a component depends on the voltage across it and the resistance, ‘R’, of that component. Resistance, measured in ohms, W, is a measure of the tendency of a component to dissipate the energy that is transmitted through it. Dissipation is the transformation of energy of one kind (e.g., electrical energy) into heat energy. This relation, V=IR, is known as ‘Ohm’s Law’.

Power Loss: P_loss= I²R = V²/R

The rate at which energy is transformed from electrical to heat energy in a conductor (and therefore lost from the electrical circuit) depends on the product of the square of the current through the conductor and the resistance of the conductor:

P_loss= I²R. That is, the power loss from a conductor is proportional to both the current and the resistance: the higher the current or resistance the more power is lost.

P= IV, V= IR,

.: P= I·IR = I²R

Alternately, Power lost is proportional to the square of the voltage across a conductor per unit of resistance: P = V²/R. That is, the same amount of voltage across a conductor will result in less power loss as the resistance is increased!

P= IV, V= IR, I = V/R,

.: P = V· V/R = V²/R

This is a less intuitive way of understanding the causes of power loss so the first formula, P= I²R, is safer to use for calculations.

Electrical Power Transformers

The need for transformers:R_Tseries= nR_ei

Electrical Power is often generated a long way away (e.g., Gippsland) from where it will eventually be used (e.g., Melbourne). This means that it needs to be transmitted through long conductors. Short (e.g., one meter long) conductors have a low resistance (e.g., 0.02 Wm^-1). Longer conductors (e.g., 100 km) may be considered to be made up of many (e.g., 100,000) low resistance resistors (e.g., 0.02 W) in series. The total effective resistance of series resistors is the sum of the individual resistors: R_Tseries= SR_i. For multiple equal resistances: R_Tseries= nR_ei (e.g., 100,000 x 0.02 = 2000 W = 2 kW). This will make power loss significant. To transmit electric power a very high voltage is needed, but to use this power a much lower voltage is needed. Transformers can be used to make these changes to the voltage of an alternating current.

Operation of a Transformer:n_p/n_s= V_p/V_s= I_s/I_p

A transformer is made up of two coils of wire wrapped around opposite sides of a hollow square/ring of iron. When one of the coils (the primary coil) is connected to an alternating current (AC) source it will produce a changing magnetic field inside the iron core, according to the Faraday-Lenz Law: e= –n Df/Dt. This will then produce a changing magnetic field inside the other coil (the secondary coil) which will induce a voltage/current in that coil: again according to the Faraday-Lenz Law: e= –n Df/Dt. If the area of the two coils is equal (as usual), then the rate of flux, Df/Dt = –e_p/n_p, produced by the primary coil will be the equal to the rate of flux,Df/Dt = –e_s/n_s, produced in the secondary coil.

.: –e_p/n_p= –e_s/n_s, .: e_p/n_p= e_s/n_s

.: e_p/e_s= n_p/n_s, P= IV, V= e= P/I,

.: n_p/n_s= (P_p/I_p) / (P_s/I_s), P_p = P_s,

.: n_p/n_s= (1/I_p) / (1/I_s) = I_s/I_p,

The ratio of primary-to-secondary coils is proportional to the ratio of the voltages and inversely to the ratio of the currents.

Transformers with n_p > n_s, are step-down, n_p < n_s, are step-up.

Ideal versus Real Transformers

These relations are true because we assumed that there was no power loss within the transformer: P_p = P_s. In reality there is always some (usually small) power loss: P_p > P_s. Some of this loss will be due to the resistance of the coils (P_loss= I²R) and some will be due to eddy currents (induced electron motion) in the iron core.

Source : http://vcephysics.wikispaces.com/file/view/Chapter+9+%286-7%29+-+Electromagnetic+Transmission+Summary.doc/30960781/Chapter%209%20%286-7%29%20-%20Electromagnetic%20Transmission%20Summary.doc

Web site link: http://vcephysics.wikispaces.com

Google key word : Electromagnetic transmission summary file type : doc

Author : not indicated on the source document of the above text

If you are the author of the text above and you not agree to share your knowledge for teaching, research, scholarship (for fair use as indicated in the United States copyrigh low) please send us an e-mail and we will remove your text quickly.