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Circuitry formulas
Ch5 Bushong
RT 244 – 12 Lect # 3
Circuit Diagram of Imaging System
Elsevier items and derived
items © 2009 by Mosby, Inc.,
an affiliate of Elsevier Inc.
2
Circuit Sections
High Voltage X-Ray Tube
Circuit
Control Console
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Line monitor
Autotransformer
Line compensator
kVp selection
mA Selection
Timing circuit
Time selection
Elsevier items and derived
items © 2009 by Mosby, Inc.,
an affiliate of Elsevier Inc.
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Step-up transformer
Rectification circuit
mA meter
X-ray tube
Filament Circuit
– Step-down transformer
– Focal spot selection
– Filaments
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Examples of Electric Circuit Elements
Elsevier items and derived
items © 2009 by Mosby, Inc.,
an affiliate of Elsevier Inc.
4
OHM’S LAW:
• V = Potential difference in volts
• I = Current in amperes
• R = Resistance in ohms ()
• V= IR
I =V/R
R=V/I
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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 unit of measure for
resistance is the ohm.
• The final important concept
Ohm's Law states that
related to the flow of
the potential difference
electricity is resistance.
(voltage) across the
Resistance is the property
total circuit or any part
of an element in a circuit
that resists or impedes the
of that circuit is equal to
flow of electricity
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.
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OHMS LAW
V = IR
• V = POTIENTAL
• A = AMPS (CURRENT)
• R = RESISTANCE (OHMS)
• WHAT MEASURES ELECTRIC POTIENTAL =
VOLT
• CURRENT = AMP
• ELECTRIC CIRCUIT IS THE PATHWAY FOR
ELECTRIC CURRENT
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Resistance ( OHM)
• The amount of opposition to flow
Conductor – material that permits electrons to
flow easily
Insulator - inhibits the flow of electrons
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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
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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 
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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
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According to Ohm’s Law,
• what would the resistance
• be if the voltage is 220 volt and the
• current is 10 ampere?
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• 100 volts of potential difference causes a
current of 2 ohms resistance
• What amperage is produced?
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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)
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PARALLEL & SERIES circuit
EX: CHRISTMAS LIGHTS
One line – all bulbs go out
Separate lines
Only bulb burns out
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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.
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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.
Elsevier items and derived
items © 2009 by Mosby, Inc.,
an affiliate of Elsevier Inc.
23
Series Circuit Formula:
•
•
•
•
Current: IT = I1 =I2 =I3
Voltage: VT = V1 + V2 + V3
Resistance:
RT = R1 + R2 + R3
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Parallel Circuit Rules
• Current:
IT = I1 + I2 + I3
• Voltage:
VT = V1 = V2 = V3
Resistance:
• 1
1 1
1
• RT = R1 + R2 + R3
• (REMEMBER TO FLIP SIDES RT/1
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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?
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Review Problems on Handout
Set up the formulas
• 4. 10 amperes
• 5. 30 volts
• 6. 2.5, 4.2, 6.8= 13.5
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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?
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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 
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• What is the total resistance
• of a parallel circuit
• with resistances of 10, 10 , 20 ?
• What about a series circuit?
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Transformer law & formulas
high voltage,
low current
Bushberg, et al., The Essential Physics of
Medical Imaging, 2nd ed., p. 126.
© UW and Brent K. Stewart PhD, DABMP
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• 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.
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Transformer Review
• Turns Ratio
NS
NP
• Step Up
– V
I
• Step Down
• Transformer Law
– V
I
N S VS I P


N P VP IS
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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
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• 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?
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• 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
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• 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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