5.1 Ohm’s Law, AC/DC Circuits, and Resistance

Nerve conduction study (NCS) instruments are voltmeters paired with current sources. The biologic signal you record is a small voltage. The pulse you deliver is a brief current. Domain II of the American Association of Electrodiagnostic Technologists (AAET) Registered Nerve Conduction Study Technologist (R.NCS.T.) outline — Basic Electronics, Instrumentation and Stimulation — is only about 5% of the exam by weight, but it decides whether every other domain’s waveforms are trustworthy. This OpenExamPrep section is independent teaching for Ohm’s law, alternating current (AC) versus direct current (DC), resistors, and electrode-skin impedance. It does not claim AAET review, partnership, or official status.

Ohm’s law: V = I × R

Ohm’s law states that voltage (V) equals current (I) times resistance (R):

V = I × R

The same relationship answers three laboratory questions when you rearrange it:

Units on the instrument:

• Voltage in volts (V). Displayed waveforms use millivolts (mV) for compound muscle action potentials (CMAPs) and microvolts (µV) for sensory nerve action potentials (SNAPs). 1 millivolt = 1,000 microvolts.
• Current in amperes (A). Stimulator panels use milliamperes (mA). 1 mA = 0.001 A.
• Resistance in ohms (Ω). Electrode checks use kilohms (kΩ). 1 kΩ = 1,000 Ω.

A convenient unit identity: mA × kΩ = V. The milli- and kilo- prefixes cancel, so 20 milliamperes through 5 kilohms is 100 volts without converting to amperes first. Use the identity as a sanity check, not as a substitute for knowing V = I × R in base units.

Worked example with lab-relevant numbers

A constant-current stimulator is set to 20 mA (0.020 A). Electrode-skin resistance under the stimulating cathode is 5 kΩ (5,000 Ω).

V = I × R = 0.020 × 5,000 = 100 V

Unit trick: 20 mA × 5 kΩ = 100 V.

If the same 20 mA is requested but the skin is poorly prepared and resistance rises to 10 kΩ:

V = 0.020 × 10,000 = 200 V

High impedance is therefore not only a “noisy screen” problem. The stimulator must generate more voltage to keep current constant. That extra voltage drop at the skin-electrode interface enlarges stimulus artifact — the shock-related deflection that can overlap or bury the response — and increases noise pickup. If the stimulator reaches its compliance voltage limit and cannot supply the needed voltage, delivered current falls below the number on the panel. The nerve is then under-stimulated even though the intensity control still reads 20 mA.

A second pass with a smaller sensory-range current: 8 mA through 2 kΩ needs only 16 V. The same 8 mA through 20 kΩ needs 160 V. Cleaning oil, light abrasion where the protocol allows, fresh gel or paste, and fully seated electrodes drop R, so the same clinical current requires less voltage and leaves a cleaner baseline.

Why high impedance increases noise conceptually: thermal (Johnson) noise grows with resistance, and a high-impedance electrode is a better antenna for ambient electric fields. Why it increases artifact: the stimulator’s larger voltage pulse couples more easily into the recording leads, and a high-impedance recording contact converts more of that coupled current into a displayed voltage (again V = I × R at the recording interface).

Alternating current (AC) versus direct current (DC)

Direct current (DC) does not reverse polarity with time. A battery is the classroom example. Slow electrode polarization and some baseline offsets behave like DC problems: the trace wanders or sits off-center until the high-pass filter (Section 5.2) removes the slow drift.

Alternating current (AC) reverses polarity at a regular frequency. North American line power is 60 hertz (Hz) AC (50 Hz in many other regions). The patient, cable loops, and the technologist act as antennas. The interference is a thick, regular ripple — 60 cycles in one second, or one cycle about every 16.7 milliseconds. Differential amplification (Section 5.2) is the main defense. A 60 Hz notch filter is a last resort because it can ring and distort CMAPs and SNAPs.

NCS stimulators deliver brief rectangular pulses of current through tissue. That pulse is not wall AC injected into the nerve. Do not confuse “we stimulate electrically” with “we are applying 60 Hz line current.” The pulse has a polarity (cathode versus anode, Section 5.3) and a duration measured in tenths of a millisecond, not a 60 Hz sine wave.

Resistors in a simple DC circuit obey Ohm’s law with a single number. Skin and electrodes in NCS are closer to impedances: they oppose pulsed and AC current with resistance plus capacitance. Machines that offer an “impedance check” are reporting that opposition, usually in kilohms. For exam teaching, treat a high kilohm reading as high opposition at that contact, whether the stem says resistance or impedance.

Resistors and electrode-skin impedance

A resistor opposes current. Skin, electrode paste, hair, oil, and the metal-electrolyte interface all act as resistors. Electrode-skin impedance is the opposition at the recording or stimulating contact.

• Low, matched impedances let the tiny biologic voltage reach the amplifier with less noise and less artifact.
• High impedance increases thermal noise, increases pickup of ambient AC, and, at stimulating electrodes, increases the voltage needed for a given current.
• Mismatched impedances between the active recording electrode and the reference convert common-mode 60 Hz into a differential voltage the amplifier cannot fully cancel. Two electrodes at 2 kΩ each behave better than one at 2 kΩ and one at 20 kΩ, even if the average looks “acceptable.”

Practical reductions: clean oil, gentle abrasion when the protocol allows, fresh conductive gel, full skin contact, quiet grouped leads, and an impedance check when the instrument provides one. Raising display gain does not fix high impedance; it only magnifies the noise.

Many laboratories teach a working target in the low kilohm range with closely matched contacts. Exact numeric cutoffs vary by machine and protocol; the exam-relevant idea is low and equal, not a single unpublished official threshold.

Series versus parallel at a basic level

Series: resistances add. Current is the same through each element; voltages add. Two 5 kΩ contacts stacked in series present 10 kΩ. Dried paste plus a loose clip is a series stack. If 10 mA flows through that 10 kΩ series path, the total voltage drop is 100 V, split across the elements.

Parallel: voltage across each branch is the same; currents add. Reciprocals add: 1/R_total = 1/R1 + 1/R2. Two equal 10 kΩ paths in parallel present 5 kΩ. A well-gelled larger contact can behave like parallel paths and lower net impedance.

Recording montages are not a textbook series circuit, but extra interfaces (hair, dried gel, corrosion on a clip) still stack like series resistance. Lowering those extras is how you lower R in Ohm’s law without changing the physiology you came to measure.

Quick numeric drill:

• 2 kΩ in series with 3 kΩ → 5 kΩ total.
• 4 kΩ in parallel with 4 kΩ → 2 kΩ total.
• 2 kΩ in parallel with 2 kΩ in parallel with 2 kΩ → 0.67 kΩ total (three equal branches).

Safety preview: current, not voltage, injures

Tissue injury and cardiac risk scale with current through the patient, not with the largest voltage printed on a power-supply sticker. Ohm’s law is the reason: I = V / R. Wet skin (low R) lets more current flow for the same voltage. A high open-circuit voltage that cannot drive current through a very high resistance is not the same hazard as a modest voltage that drives tens of milliamperes across the thorax.

Keep stimulators connected only when you intend to stimulate. Do not assume “it is only a few volts” if a current path exists through the patient. Macroshock, leakage current, isolated power, and grounding rules belong in the electrical-safety chapter; this section only plants the electronics fact those rules rest on: current injures. Read the later safety chapter before you treat this preview as complete.