# Circuitry formulas Ch5 Bushong RT 244 – 12 Lect # 3.

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Circuitry formulas Ch5 Bushong RT 244 – 12 Lect # 3

Elsevier items and derived items © 2009 by Mosby, Inc., an affiliate of Elsevier Inc. 2 Circuit Diagram of Imaging System

Elsevier items and derived items © 2009 by Mosby, Inc., an affiliate of Elsevier Inc. 3 Circuit Sections Control Console – Line monitor – Autotransformer – Line compensator – kVp selection – mA Selection – Timing circuit – Time selection High Voltage X-Ray Tube Circuit – Step-up transformer – Rectification circuit – mA meter – X-ray tube Filament Circuit – Step-down transformer – Focal spot selection – Filaments

Elsevier items and derived items © 2009 by Mosby, Inc., an affiliate of Elsevier Inc. 4 Examples of Electric Circuit Elements

5 OHM’S LAW: V = Potential difference in volts I = Current in amperes R = Resistance in ohms (  ) V= IR I =V/R R=V/I

properties of electricity. voltage, current, and resistance the units of measure for electric potential (voltage) and current (amperage) are the same units we use as technologists to express technical factors on the x-ray machine operating console. kVp is kilovoltage peak and mA is milliamperes.

voltage Voltage is an expression of electric potential. As stated in the previous section, electric potential is the ability to do work due to separation of charges Electric potential is measured in volts. The term volt is from the name of the Italian physicist, Volta, who invented the battery two centuries ago. This unit is a measure of the difference in electric potential between two points. The volt is equal to the amount of work (joules) that can be done per unit of charge

Current Current is the actual flow of electrons in a conductor. People sometimes mistakenly use the word "volt" as if it referred to the current passing through a conductor. the volt refers to the difference in electric potential between the two charges that make the current flow. The actual flow of electrons is current.

Amperes = columbs/sec Current is measured in terms of the rate of electron flow. This is how much electric charge flows past a particular point in one second. The SI unit for charge per second is the ampere, sometimes just called an "amp." One ampere equals one coulomb flowing by in one second: Voltage and amperes are related in terms of how they affect the strength of an electric current. A low-voltage, high-amperage current has many electrons moving but a low-amperage, high-voltage current with fewer electrons moving may be just as powerful because of the higher potential.

resistance The final important concept related to the flow of electricity is resistance. Resistance is the property of an element in a circuit that resists or impedes the flow of electricity The unit of measure for resistance is the ohm. Ohm's Law states that the potential difference (voltage) across the total circuit or any part of that circuit is equal to the current (amperes) times the resistance. It is expressed by the formula V= IR, where V is voltage, I is current, and R is resistance.

11 OHMS LAW V = IR V = POTIENTAL A = AMPS (CURRENT) R = RESISTANCE (OHMS)

12 WHAT MEASURES ELECTRIC POTIENTAL = VOLT CURRENT = AMP ELECTRIC CIRCUIT IS THE PATHWAY FOR ELECTRIC CURRENT

13 Resistance ( OHM) The amount of opposition to flow Conductor – material that permits electrons to flow easily Insulator - inhibits the flow of electrons

14 V = IR The voltage across the total circuit or any portion of the circuit is equal to the current times the resistance. According to Ohm’s Law, what would the voltage be if the resistance is 2  and the current is 4 ampere? A. 2 volt B. 4 volt C. 8 volt D. 10 volt

15 R = V/I The resistance in a circuit is equal to the voltage divided by the current According to Ohm’s Law, what would the resistance be if the voltage is 110 volt and the current is 5 ampere? A. 22  B. 55  C. 220  D. 550 

16 I = V/R The current across a circuit is equal to the voltage divided by the resistance. According to Ohm’s Law, what would the current be if the voltage is 12 volt and the resistance is 1.5  ? A. 2 Ampere B. 4 Ampere C. 6 Ampere D. 8 Ampere

17 According to Ohm’s Law, what would the resistance be if the voltage is 220 volt and the current is 10 ampere?

18 100 volts of potential difference causes a current of 2 ohms resistance What amperage is produced?

19 X-ray Tubes have complicated wiring SERIES CIRCUIT (all circuit elements are connected in a line along the same conductor PARALLEL CIRCUIT (elements bridge the circuit rather than lie in a line along the conductor)

20 PARALLEL & SERIES circuit EX: CHRISTMAS LIGHTS One line – all bulbs go out Separate lines Only bulb burns out

Rules for Simple Series Circuits The total resistance is equal to the sum of the individual resistances. The current through each circuit element is the same and is equal to the total circuit current. The sum of the voltages across each circuit element is equal to the total circuit voltage. Elsevier items and derived items © 2009 by Mosby, Inc., an affiliate of Elsevier Inc. 22

Elsevier items and derived items © 2009 by Mosby, Inc., an affiliate of Elsevier Inc. 23 Rules for Parallel Circuit The sum of the currents through each circuit element is equal to the total circuit current. The voltage across each circuit element is the same and is equal to the total circuit voltage. The total resistance is the inverse of the sum of the reciprocals of each individual resistance.

24 Series Circuit Formula: Current: I T = I 1 =I 2 =I 3 Voltage: V T = V 1 + V 2 + V 3 Resistance: RT = R 1 + R 2 + R 3

25 Parallel Circuit Rules Current: I T = I 1 + I 2 + I3 Voltage: VT = V1 = V2 = V3 Resistance: 1 1 1 1 R T = R1 + R2 + R3 (REMEMBER TO FLIP SIDES R T /1

26 Review Problems on Handout Set up the formulas 4. What is the total current in a series circuit with 3 resistances, each supplied with 10 amperes? 5. What is the total voltage in a series circuit with 3 resistances, each supplied with 10 volts? 6. What is the total resistance of a series circuit with resistances of 2.5 , 4.2 , 6.8  ?

27 Review Problems on Handout Set up the formulas 4. 10 amperes 5. 30 volts 6. 2.5 , 4.2 , 6.8  = 13.5

28 Review Problems on Handout Set up the formulas 7. What is the total current in a parallel circuit with 3 resistances, each supplied with 10 amperes? 8. What is the total voltage in a parallel circuit with 3 resistances, each supplied with 10 volts? 9. What is the total resistance of a parallel circuit with resistances of 2.5 , 4.2 , 6.8  ?

29 Review Problems on Handout Set up the formulas 7. 30 amperes 8. 10 volts 9. 1/2.5 , 1/4.2 , 1/ 6.8  = 0.4 +.24 + 0.14 =.79/1 = 1.26 

30 What is the total resistance of a parallel circuit with resistances of 10 , 10 , 20  ? What about a series circuit?

Transformer law & formulas 31 © UW and Brent K. Stewart PhD, DABMP 31 Bushberg, et al., The Essential Physics of Medical Imaging, 2nd ed., p. 126. high voltage, low current

The number of turns in the primary and secondary coils of a transformer determines whether it will increase or decrease voltage and by how much. In other words, the number of turns in the coil "cut" by this magnetic field determines the magnitude of the induced voltage as reflected by the transformer law formula: Vs/Vp = Ns/Np (Where V is voltage, N is the number of turns, s is secondary coil, and p is primary coil.) For example: A transformer has 100 turns in the primary coil and 10,000 turns in the secondary coil (a turns ratio of 10,000/100 or 100/1). If 500V is applied to the primary side, what will the output voltage be? Calculate as follows: Vs/500V = 10,000/100 Vs/500V = 100/1 Vs = 500V x 100 = 50,000V Simply stated, if there are more turns in the secondary coil than in the primary coil, voltage will be increased. The opposite is also true: If there are more turns in the primary coil than in the secondary coil, voltage will be reduced. 32

33 Transformer Review Turns Ratio Transformer Law Step Up –  V  I Step Down –  V  I

34 TRANSFORMER FORMULAS (STEP UP OR DOWN) V = voltage N = # turns p = primary s = secondary I = current Vp = N p Vs Ns Vp = I s Vs Ip Np = I s Ns Ip

35 Transformer has a turns ratio of 1 to 200. There are 250 volts on the primary side, what is the voltage on the secondary side?

36 The Transformer has 100 turns on the Primary side, 100 volts and 10 amps. The secondary side has 50,000 turns of wire. What is the current AND voltage supplied to the secondary side? ____________ volts = ________ kVp __________ amps = ________mA

37 A radiograph using 200 ma 1/20 sec 55 kvp of a hand was taken in a 3Ø 12p room. What do you use in a single phase room?

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