Ohm’s law

7 min read Last updated April 8, 2026

Clinical relevance in anaesthesia

  • Electrical safety and fault currents: magnitude of current through a person depends on applied voltage and total resistance/impedance
    • Higher voltage or lower resistance → higher current → increased risk of macroshock (e.g. mains fault) and microshock (invasive lines)
    • Skin resistance varies widely (dry vs wet/abraded), so current can rise dramatically in wet conditions
  • Defibrillation/pacing: delivered current depends on transthoracic impedance; energy setting is not the same as current delivered
    • High impedance (poor pad contact, small pads, hairy/dry skin) reduces current for a given voltage waveform
  • Electrosurgery/diathermy: tissue heating relates to current and resistance (Joule heating)
    • Power deposition in tissue: P = I²R (or P = V²/R) explains burns at high resistance points (small contact area, poor return electrode contact)
  • Monitoring and equipment: understanding voltage drops and current draw helps interpret fuses, circuit breakers, and device power ratings
    • Mains current drawn by a device: I = P/V (approx for resistive loads); real devices may have power factor effects (AC)

Core statement and definitions

  • Ohm’s law: for a conductor at constant temperature and physical conditions, current is proportional to potential difference across it
  • Equation: V = I R
    • V: potential difference (volt, V) = energy per unit charge (J C⁻¹)
    • I: current (ampere, A) = rate of flow of charge (C s⁻¹)
    • R: resistance (ohm, Ω) = opposition to current flow (for DC); in AC, opposition is impedance (Z, Ω)
  • Rearrangements: I = V/R; R = V/I

Ohmic vs non-ohmic behaviour

  • Ohmic conductor: V–I relationship is linear; resistance is constant (straight line through origin on V vs I plot)
  • Non-ohmic: resistance changes with voltage/current/temperature; V–I curve is non-linear
    • Examples: filament lamp (R increases with temperature), semiconductor diode (directional, threshold), many biological tissues (complex impedance)
  • Clinical implication: human body is not a fixed resistor; impedance varies with frequency (AC), hydration, contact area, and skin condition

Related power and energy equations (commonly examined with Ohm’s law)

  • Electrical power: P = VI
  • Using Ohm’s law: P = I²R and P = V²/R
    • Explains why high current causes heating (I² term) and why high resistance at a contact point can cause burns (P = I²R locally)
  • Energy: E = Pt (joule, J); in defibrillation, selected energy (J) does not uniquely determine delivered current (depends on impedance and waveform)

Resistance: determinants and combinations

  • Material/geometry: R = ρL/A
    • ρ resistivity (Ω·m), L length (m), A cross-sectional area (m²)
    • Temperature dependence: metals typically increase R with temperature; electrolytes/tissues can behave differently
  • Series resistors: R_total = R1 + R2 + …; current is the same through each component
    • Voltage divides in proportion to resistance: V1/V2 = R1/R2
  • Parallel resistors: 1/R_total = 1/R1 + 1/R2 + …; voltage is the same across each branch
    • Current divides inversely with resistance: I1/I2 = R2/R1
    • Adding parallel paths reduces total resistance (increases total current for a given voltage)

AC note: impedance and limitations of simple Ohm’s law

  • For AC circuits, use impedance: V = IZ (phasor form); Z includes resistance and reactance (capacitive/inductive)
  • Capacitive reactance: Xc = 1/(2πfC) (decreases with frequency); inductive reactance: Xl = 2πfL (increases with frequency)
  • In many FRCA calculations, devices are approximated as resistive unless stated; be explicit about assumptions
State Ohm’s law and the conditions under which it applies. How would you demonstrate it experimentally?

This is a common physics viva stem: definition + assumptions + practical demonstration and graph interpretation.

  • Statement: current through a conductor is proportional to the potential difference across it, provided temperature and physical conditions remain constant
  • Equation: V = IR; constant of proportionality is resistance R
  • Demonstration: variable DC supply + ammeter in series + voltmeter across resistor; vary V and record I
  • Plot V vs I: straight line through origin for an ohmic conductor; gradient = R (if plotting V on y-axis)
  • If temperature rises (e.g. filament lamp), V–I becomes non-linear because R changes
A device is rated 60 W on a 240 V supply. Assuming it behaves as a resistive load, calculate the current drawn and its resistance.
  • Use P = VI → I = P/V = 60/240 = 0.25 A
  • Then R = V/I = 240/0.25 = 960 Ω (equivalently R = V²/P = 240²/60 = 960 Ω)
  • Examiner may ask limitation: many real loads are not purely resistive on AC (power factor), but this is the standard FRCA assumption unless stated
Explain why wet skin increases the risk of electric shock. Use Ohm’s law to support your answer.
  • For a given voltage exposure, current is I = V/R
  • Wet/abraded skin reduces resistance substantially (stratum corneum barrier compromised), so current increases
  • Higher current increases risk of ventricular fibrillation, respiratory tetany, and burns; severity relates more to current magnitude and path than voltage alone
Two resistors, 2 kΩ and 3 kΩ, are connected (a) in series and (b) in parallel across a 12 V supply. Calculate total resistance and total current in each case.
  • Series: R_total = 2k + 3k = 5 kΩ; I_total = V/R = 12/5000 = 0.0024 A = 2.4 mA
  • Parallel: 1/R_total = 1/2000 + 1/3000 = (3+2)/6000 = 5/6000 → R_total = 1200 Ω
  • Parallel current: I_total = 12/1200 = 0.01 A = 10 mA
A patient has a transthoracic impedance of 80 Ω. A defibrillator delivers a (simplified) 2000 V pulse across the chest. Estimate the peak current. What happens if impedance increases to 120 Ω?

FRCA-style: apply Ohm’s law to a simplified defibrillation model; acknowledge simplification (real waveforms are time-varying).

  • At 80 Ω: I = V/R = 2000/80 = 25 A
  • At 120 Ω: I = 2000/120 ≈ 16.7 A
  • Higher impedance reduces delivered current (and thus myocardial current density), potentially reducing efficacy; improve pad contact/position, use gel, remove hair
A return electrode (diathermy plate) has poor contact, leaving only a small area conducting. Using P = I²R, explain why this increases burn risk at the plate.
  • If contact area decreases, effective resistance at the skin–electrode interface increases (R = ρL/A concept)
  • For a given diathermy current, local heating power increases: P = I²R at the high-resistance interface
  • Current density increases when area is small, concentrating heating and increasing risk of thermal injury
Describe the difference between resistance and impedance, and how Ohm’s law is modified for AC circuits.
  • Resistance (R): opposition to DC current; dissipates power as heat
  • Impedance (Z): total opposition to AC current; includes resistance and reactance (capacitive/inductive), and is frequency-dependent
  • AC form: V = IZ (phasor relationship); voltage and current may be out of phase
A 9 V battery is connected across a resistor and the measured current is 3 mA. Calculate the resistance. If the resistor warms and the current falls to 2 mA, what is the new resistance and what does this suggest about the material?
  • Initial R = V/I = 9/0.003 = 3000 Ω (3 kΩ)
  • After warming: R = 9/0.002 = 4500 Ω (4.5 kΩ)
  • Resistance increased with temperature → typical of metallic conductors/filaments (positive temperature coefficient); behaviour may become non-ohmic if temperature changes significantly
A 1 kΩ resistor is placed in series with a 2 kΩ resistor across a 12 V supply. Calculate the voltage across each resistor.
  • Total resistance = 3 kΩ; current I = 12/3000 = 4 mA
  • Voltage across 1 kΩ: V1 = IR1 = 0.004 × 1000 = 4 V
  • Voltage across 2 kΩ: V2 = IR2 = 0.004 × 2000 = 8 V (check: 4 + 8 = 12 V)
Explain why ‘high voltage’ is not the same as ‘high danger’. Use Ohm’s law and give clinical examples.
  • Physiological harm relates primarily to current through the body and its pathway/duration: I = V/R
  • High voltage sources can be relatively safe if current is limited (high internal resistance) or contact is brief; conversely, low voltage can be dangerous if resistance is low and current is high
  • Examples: static electricity is very high voltage but tiny charge/current; a 12 V car battery is low voltage but can deliver very high currents through low resistance (burns/arc hazards)
  • In theatre: microshock risk in patients with intracardiac conductors—very small currents can be hazardous because the effective resistance/path to myocardium differs

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