Voltage, Current, Resistance, and Power: Ohm's Law, Series and Parallel
Unit 4: Electricity, Electronics, and Imaging Power. Lesson 14 of 60 in CRES Academy.
Every measurement you will ever take on an imaging system comes back to four quantities and one law. The scale is bigger than on a monitor bench, but the arithmetic is the same.
The four quantities
- Charge is the quantity of electricity; current is charge in motion.
- Current (I), in amperes, is electric current: charge in motion. Tube current is in milliamperes and filament current in amperes.
- Voltage (V), in volts, is the pressure that pushes the flow, and its older name, electromotive force, says exactly what it does. Tube potential is in kilovolts.
- Resistance (R), in ohms, opposes the flow, and electric resistance in a wire, a contact, or a winding is where unwanted heat comes from.
The water analogy holds: voltage is pressure, current is the flow rate, resistance is the narrowness of the pipe, and power is the work the water does when it arrives.
Energy and charge, before the law
Energy is the ability to do work, and the law of conservation says it changes form rather than disappearing. On a service call you meet it as potential energy in a raised table or a charged capacitor, kinetic energy in a moving gantry, thermal energy in an anode, electrical energy in every circuit you measure, chemical energy in a battery pack, and nuclear energy in the tracer a gamma camera watches.
Electrostatics is charge at rest. Three laws of electrostatics are worth carrying: unlike charges attract and like charges repel, charge on a conductor sits on its outer surface, and the force between two charges falls with the square of the distance between them. Electrification is how an object gains that charge, and the methods of electrification are friction, contact, and induction, which is why a plastic cover attracts dust to a detector and why you ground yourself before handling a board. Electrodynamics is the same charge in motion, and that is the rest of this unit.
Ohm's law and power
V = I x R I = V / R R = V / I P = V x I P = I squared x R P = V squared / R in watts Imaging power (mA x kVp) / 1000 = kW, and multiply by 0.7 for a single-phase generator
Worked: 24 V across 8 ohms draws 3 A and dissipates 72 W. A 1,000 mA station at 120 kVp is (1000 x 120) / 1000 = 120 kW, which is why the room needs a feeder of its own.
Series and parallel
Two electric circuits cover nearly everything in a generator cabinet, and telling them apart decides what a measurement means.
- Series is one path. The same current flows through every element, the voltage drops add up to the source, and resistances add: R total = R1 + R2 + R3. One open element stops everything, which is exactly how a fuse and an interlock chain work.
- Parallel is several paths across the same two points. Every branch sees the same voltage, the branch currents add, and the reciprocals add: 1 / R total = 1/R1 + 1/R2. Total resistance is always less than the smallest branch, so two 100 ohm elements in parallel measure 50 ohms. Receptacles, cabinet fans, and the low-voltage loads inside a generator are parallel, which is why one can fail without the others noticing.
The numeric prefixes you have to read without thinking
kilo x 1000 kV (tube potential), kW (power), kohm (resistance) milli x 0.001 mA (tube current), ms (exposure time), mSv (dose) micro x 0.000001 microamps (leakage limits), microfarads (capacitors)
So 70 kV is 70,000 V, 500 mA is 0.5 A, 10 ms is 0.01 s, and 500 microamps is 0.0005 A.
Measuring without damaging anything
- Volts are measured across a component with the circuit live, meter in parallel, one hand in your pocket.
- Amps are measured in series, in the path, or without breaking it using a clamp.
- Ohms and continuity are measured with the equipment off, isolated, and capacitors discharged; a reading over the meter's limit means the path is open.
Never put a meter rated for the bench across a high-voltage section, and never trust a console display for a quality control number.
Generator-scale examples
- The filament circuit is low voltage and high current: about 4 A or more through a coil of a fraction of an ohm, and small resistance changes there move tube current a long way.
- Tube current is set by that filament temperature, not by a rheostat in the high-voltage path.
- Kilovolts come from a step-up transformer, so the primary side carries hundreds of volts at high current while the secondary carries tens of kilovolts at milliamperes. Power is roughly conserved, which is the cross-check when a reading looks impossible.
Voltage, Current, Resistance, and Power: Ohm's Law, Series and Parallel, explained slowly
The same four quantities, at a different scale
A monitor bench deals in volts and milliamperes. An imaging generator deals in kilovolts and amperes in the same machine, sometimes in the same cabinet, and the only thing that changes is the size of the numbers and the consequence of a mistake. The law does not change.
Quantity Symbol Unit Where you meet it in imaging Charge Q coulomb what a capacitor bank holds, and what crosses the tube Current I ampere tube current in mA, filament current in A, leakage in microamps Voltage V volt tube potential in kV, control rails in VDC, mains in VAC Resistance R ohm filament a fraction of an ohm, ground path under 0.5 ohm Power P watt a generator station in kW, a board's rail in a few watts
The water analogy carries you a long way: voltage is pressure, current is flow, resistance is the narrowness of the pipe, power is the work the water does when it arrives. A high-voltage section is high pressure and low flow; a filament circuit is low pressure and high flow.
Energy, charge at rest, and charge in motion
Energy is the ability to do work, and the law of conservation of energy says it only changes form. The forms are all in the department: potential energy in a raised table, a counterweight, or a charged capacitor bank; kinetic energy in a gantry that is already moving when you reach for it; thermal energy in an anode at the end of a run; electrical energy in everything you measure; chemical energy in a portable's battery pack; and nuclear energy in the tracer a gamma camera watches. Nothing on a service call is created or destroyed, only moved, which is why heat has to go somewhere and why a capacitor still holds what you put into it an hour ago.
Electrostatics is charge sitting still. The laws of electrostatics are short: unlike charges attract and like charges repel, charge on a conductor migrates to its outer surface, and the force between two charges falls off with the square of the distance between them. Electrification is how something acquires charge, and the methods of electrification are three: friction, contact, and induction. All three are practical rather than academic here. Friction on a plastic cover is why dust ends up on a detector face. Contact is why you take a shock off a cart in a dry corridor in February. Induction is why a charged object can affect a nearby board without touching it, and why ESD precautions are a procedure and not a superstition. Electrodynamics is that same charge in motion, and from here on the whole unit is electrodynamics.
Ohm's law and power, with the rearrangements
V = I x R I = V / R R = V / I P = V x I P = I squared x R P = V squared / R (mA x kVp) / 1000 = kW x 0.7 for a single-phase generator
Worked problems at the scale you will actually see:
- 24 V across 8 ohms: I = 24 / 8 = 3 A, P = 24 x 3 = 72 W.
- A 1,000 mA station at 120 kVp: (1000 x 120) / 1000 = 120 kW. That is why the room needs its own feeder.
- The same station on a single-phase generator: 120 x 0.7 = 84 kW of useful rating.
- A filament drawing 4 A through 0.5 ohm: V = 4 x 0.5 = 2 V, P = 4 squared x 0.5 = 8 W. Low voltage, high current, and all of it as heat, which is the point.
- A 500 microamp leakage current through a 1,000 ohm body path: V = 0.0005 x 1000 = 0.5 V. Small, which is why the limit is set where it is.
Series and parallel, and what each failure looks like
Series Parallel Current the same everywhere divides between branches, branch currents add Voltage drops add to the source the same across every branch Resistance R1 + R2 + R3 1/Rt = 1/R1 + 1/R2; always less than the smallest Open element everything stops only that branch stops Short element the rest sees more voltage the source sees a fault current Imaging example interlock chain, fuse, filament receptacles, cabinet fans, low-voltage loads
That table is a troubleshooting tool. "Nothing happens at all" with no fault code is a series problem: a chain with one open link. "One thing is dead and everything else is fine" is a parallel branch.
Prefixes, read without thinking
kilo x 1,000 70 kV = 70,000 V 120 kW = 120,000 W 10 kohm = 10,000 ohm milli x 0.001 500 mA = 0.5 A 10 ms = 0.01 s 1 mSv = 0.001 Sv micro x 0.000001 500 microamps = 0.0005 A 100 microfarads = 0.0001 F
Half the arithmetic mistakes on the exam are prefix mistakes, not algebra mistakes. Convert everything to base units before you multiply, then convert back at the end.
Measuring without hurting yourself or the machine
- Volts: meter in parallel, across the component, circuit live. One hand clear, the right meter category for the voltage, and never the bench meter across a high-voltage section.
- Amps: meter in series, in the path, or a clamp around the conductor so nothing is broken. Never put an ammeter across a live source.
- Ohms and continuity: equipment off, isolated, capacitors discharged. An over-range reading means the path is open, which is how you walk an interlock chain.
- Compare against the printed value at the test point, not against your expectation.
- Never trust a console display for a quality control number; the display shows what was selected, not what happened.
What to memorize
- V = I x R, P = V x I, P = I squared x R, P = V squared / R.
- Series: same current, voltages add, resistances add, one open stops everything. Parallel: same voltage, currents add, total less than the smallest branch.
- kilo, milli, micro; convert to base units before calculating.
- Volts across live, amps in series, ohms with the power off and capacitors discharged.
- Imaging power in kilowatts is mA times kVp over 1000, times 0.7 for single phase.