# Magnetic Flux (primary) = Magnetic Flux (secondary) Eq 2

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1 Transformers Electrical transformers are used to transform voltage or current. The basic arrangement is shown in Figure 1 and 2 below. The best a transformer can do is to transfer all of the electrical energy (or power) from the primary coil to the secondary. An equation for this statement is equivalent to: The physics behind the operation of a transformer is the magnetic flux ( ) coupling between the primary and secondary coils. Because of the coupling of the 2 coils, the magnetic flux change within the primary coil is also that of the secondary coil. Magnetic Flux (primary) = Magnetic Flux (secondary) Eq 2 We assume that the coil's resistance is very small so the EMF generated is equivalent to the output voltage V. This gives a simple relation between the primary and secondary voltages

2 In a step-up transformer N2>N1 resulting in a voltage increase at the secondary output terminal. In a step-down transformer N2<N1 and the voltage is decreased. A transformer is a kind of electrical lever. In a mechanical lever the correct arrangement can amplify force but the Work=Force x Distance (or power) at the output can never be greater than at the input. A lever arrangement could also be used to amplify distance or speed when we interchange the input and output of a force-increase lever. For an electrical transformer conservation of energy (Equation 1) requires that as the voltage is increased at the secondary coil for a step up transformer, the current is decreased. Likewise a voltage reduction in a step down transformer can result in much larger currents. Combining Equations 1 and Equations 3 give

3 Question 1. A step-down transformer is used for recharging the batteries of portable devices such as cell phones. The turns ratio inside the transformer is 10:1 and it is used with 120-V (rms) household service. If a particular ideal transformer draws 0.50 A from the house outlet, what are (a) the voltage supplied to the cell phone and (b) the current supplied to the cell phone from the transformer? (c) How much power is delivered? Commonly Step-down transformers are used for toys and other house hold items because they convert 120 volts to 6 to 9 volts. The 120 volt source can give you a respectable shock whereas a 6 to 9 volt source will not. Often the AC voltage is converted to DC using a diode and a capacitor. The diode allows current to flow in one direction only so the bottom of the sine wave voltage function is chopped off. A diode is like a one-way valve. The solid line of the current versus time graph at left would be the output of the transformer with only a diode (no capacitor). The capacitor essentially smooths out the signal. In the figure at left R represents the

4 resistance of the device you will be operating with the transformer. Often transformers use laminated iron cores to couple the magnetic flux between the primary and secondary coils. This limits the energy loss due to eddy currents building up in the core. The laminations limit the size of the eddy currents. Step-up transformers are often used for electric power transmission. They are also used in neon signs, automobiles for spark, and other high voltage applications. Question Mega-Watt of power (P=1,000,000 Watts) is to be transmitted to a city 80 km from the power generator along an aluminum wire. The total resistance of this transmission line (160 km total length) is a) If this power is transmitted at 5,000 Volts how much current will be required? b) How much power will be lost as heat when transmitting this energy at

5 5,000 Volts. c) If a step-up transformer is used to transmit this power at 300,000 Volts, how much current will be required? d) How much power will be lost as heat when transmitting this energy at 200,000 Volts? e) if the transformer used has 1000 coils in the primary what is the required number of turns in the secondary coil? Step-down transformers are also used for electric power transmission or in other situations where either low voltage is desired for safety or high current is needed and in arc welders. Question 3. A power pole transformer is used to decrease the 12,000 volt transmission voltage into a safer 120 volt signal. a) If the primary coil has 10,000 turns, what is the required number of turns in the secondary coil? b) when houses in the neighborhood draw 800 A of current from the secondary, how much current will there be in the primary coil of this

6 transformer? Answers Question 1. A step-down transformer is used for recharging the batteries of portable devices such as cell phones. The turns ratio inside the transformer is 10:1 and it is used with 120-V (rms) household service. If a particular ideal transformer draws 0.50 A from the house outlet, what are (a) the voltage supplied to the cell phone and V=120.0 /10=12 Volts (b) the current supplied to the cell phone from the transformer? I=0.5 A(10)=5 A (c) How much power is delivered? P=IV=.5A*120V=60 Watts

7 Question Mega-Watt of power (P=1,000,000 Watts) is to be transmitted to a city 80 km from the power generator along an aluminum wire. The total resistance of this transmission line (160 km total length) is a) If this power is transmitted at 5,000 Volts how much current will be required? P=IV 1,000,000=I(5,000) I=200A b) How much power will be lost as heat when transmitting this energy at 5,000 Volts. V=IR=200A(10 )=2000 Volts P=IV=200A(2000V)=400,000 Watts (about 40% of the total power) c) If a step-up transformer is used to transmit this power at 200,000 Volts, how much current will be required? \ P=IV 1,000,000=I(200,000) I=5A d) How much power will be lost as heat when transmitting this energy at 200,000 Volts? V=IR=5A(10 )=50 Volts P=IV=5A(50V)=250 Watts (insignificant loss)

8 e) if the transformer used has 1000 coils in the primary what is the required number of turns in the secondary coil? N2/N1=V2/V1=200000/5000=40 So N2=40N1=40(1000)=40,000 Question 3. A power pole transformer is used to decrease the 12,000 volt transmission voltage into a safer 120 volt signal. a) If the primary coil has 10,000 turns, what is the required number of turns in the secondary coil? Step-down by 100 so 10,000/100=N2=100 b) when houses in the neighborhood draw 800 A of current from the secondary, how much current will there be in the primary coil of this transformer? Current is secondary (households is higher by 100) so 8 A in primary

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