Capacitance and inductance

7 min read Last updated April 8, 2026

Why anaesthetists care

  • Capacitance and inductance determine how circuits respond to changing voltages/currents (transients), affecting monitoring, defibrillation, diathermy, pacing and electrical safety.
  • Capacitive effects: ECG/pressure transducer filtering, electrode–skin interface, cable coupling, defibrillator energy storage, stray capacitance causing leakage currents.
  • Inductive effects: diathermy/EMI, transformers in isolated power supplies, inductive coupling into ECG leads, inrush currents, inductive reactance in AC circuits.
  • Both are frequency-dependent: they explain why high-frequency interference behaves differently from mains frequency and DC.

Clinical examples

  • Defibrillator: capacitor charged to high voltage then discharged through patient; energy depends on capacitance and voltage.
    • Biphasic waveforms shape current delivery; circuit time constants influence peak current and duration.
  • Electrosurgery (diathermy): high-frequency current reduces neuromuscular stimulation; capacitive/inductive coupling can cause burns or artefact.
    • Long parallel cables increase coupling; keep ECG/SpO2 cables away from diathermy leads; use short, separated runs.
  • ECG artefact: mains pickup and diathermy interference via capacitive coupling; monitor input circuits use RC filtering and high input impedance.
  • Isolation transformers: inductive devices providing galvanic isolation; reduce shock risk but do not eliminate leakage via stray capacitance.

Capacitance: core concepts

  • Definition: ability to store charge per unit potential difference.
  • Unit: farad (F) = coulomb per volt; clinically common values are microfarads to nanofarads in equipment; stray capacitances are often pF–nF.
  • Parallel plate capacitor: C = εA/d where ε = ε0εr.
    • Increase C by increasing plate area A, decreasing separation d, or increasing dielectric constant εr.
  • Energy stored: E = 1/2 C V^2 (important for defibrillators).
  • Current–voltage relationship: i = C (dV/dt). Capacitor opposes change in voltage; current leads voltage by 90° in AC.
  • Capacitive reactance: Xc = 1/(2πfC). High at low frequency (blocks DC), low at high frequency (passes AC).

RC circuits and time constant

  • Time constant: τ = RC (seconds). Determines speed of charging/discharging.
  • Charging (step input V): Vc(t) = V(1 − e^(−t/RC)); current decays exponentially.
    • At t = τ: Vc ≈ 63% of final value; at 3τ ≈ 95%; at 5τ ≈ 99%.
  • Discharging: Vc(t) = V0 e^(−t/RC).
  • Filtering: RC low-pass (output across C) attenuates high frequencies; RC high-pass (output across R) attenuates low frequencies.
    • Cut-off frequency (−3 dB): fc = 1/(2πRC).

Inductance: core concepts

  • Definition: property of a conductor/coil whereby a change in current induces an opposing emf (Lenz’s law).
  • Unit: henry (H) = volt-second per ampere.
  • Induced emf: V = L (dI/dt). Inductor opposes change in current; voltage leads current by 90° in AC.
  • Inductive reactance: Xl = 2πfL. Low at low frequency (passes DC), high at high frequency (impedes AC).
  • Energy stored in magnetic field: E = 1/2 L I^2.

RL circuits and time constant

  • Time constant: τ = L/R (seconds).
  • Current rise with step voltage V: i(t) = (V/R)(1 − e^(−tR/L)).
    • At t = τ: current ≈ 63% of final value.
  • Current decay when supply removed: i(t) = I0 e^(−tR/L).
  • Switching transients: interruption of current in an inductor can generate high voltages (V = L dI/dt) → arcing; mitigated by snubber circuits/diodes.

RLC resonance (high-yield)

  • In series RLC, resonance occurs when Xl = Xc; impedance is minimum and current is maximal (limited by R).
  • Resonant frequency: f0 = 1/(2π√(LC)).
  • Clinical relevance: frequency-selective circuits in filters, oscillators, and some monitoring/telemetry systems; also explains peaks in EMI susceptibility.

AC phase relationships and impedance

  • Capacitor: current leads voltage by 90°; inductor: current lags voltage by 90°.
  • Impedance: Z combines resistance and reactance (vector/phasor). For series circuits: |Z| = √(R^2 + (Xl − Xc)^2).
  • Power: real power dissipated in R; reactive power oscillates in L/C fields; power factor worsens when reactance dominates.

Capacitive and inductive coupling (equipment safety/artefact)

  • Capacitive coupling: electric field between conductors separated by an insulator; increases with higher frequency, larger area, smaller separation, longer parallel run.
  • Inductive coupling: changing magnetic field from a current-carrying conductor induces voltage in nearby loop; increases with higher dI/dt, larger loop area, closer proximity, longer parallel run.
  • Mitigation: minimise loop area (twist leads), keep cables short, avoid parallel runs, increase separation, shielding, proper earthing, use differential inputs and filters.
Define capacitance. Give its unit and derive the relationship between current and voltage for a capacitor.

Core definitions and the key differential equation are frequently examined.

  • Capacitance: charge stored per unit potential difference.
  • Unit: farad (F) = coulomb per volt.
  • From Q = CV, differentiate: dQ/dt = C dV/dt. Since i = dQ/dt, then i = C dV/dt.
  • Interpretation: capacitor resists change in voltage; rapid voltage changes produce large currents.
A past-style question: Describe the charging and discharging of a capacitor through a resistor, including the meaning of the time constant.

Expect exponential equations and the 63% rule.

  • Time constant: τ = RC (s).
  • Charging to a step voltage V: Vc(t) = V(1 − e^(−t/RC)).
  • Discharging from V0: Vc(t) = V0 e^(−t/RC).
  • At t = τ: 63% charged (or 37% remaining on discharge); ~95% at 3τ; ~99% at 5τ.
A past-style question: What is capacitive reactance? How does it vary with frequency and what does that mean for DC vs AC?
  • Capacitive reactance: opposition to AC due to capacitance.
  • Xc = 1/(2πfC).
  • As frequency increases, Xc decreases: capacitor passes high-frequency signals more readily.
  • At f = 0 (DC), Xc → ∞: ideal capacitor blocks DC once fully charged.
Define inductance. Give its unit and the relationship between voltage and rate of change of current.
  • Inductance: property whereby a changing current induces an emf opposing that change (Lenz’s law).
  • Unit: henry (H) = V·s/A.
  • Induced voltage: V = L (dI/dt).
  • Interpretation: inductor resists change in current; rapid current interruption can generate large voltages.
A past-style question: Describe current growth and decay in an RL circuit and define the time constant.
  • Time constant: τ = L/R (s).
  • Current rise after step voltage V: i(t) = (V/R)(1 − e^(−tR/L)).
  • Current decay after supply removed: i(t) = I0 e^(−tR/L).
  • At t = τ: current reaches ~63% of final value (or decays to 37%).
A past-style question: Compare capacitors and inductors in AC circuits (phase, frequency behaviour, energy storage).
  • Phase: capacitor current leads voltage by 90°; inductor current lags voltage by 90°.
  • Frequency: Xc = 1/(2πfC) decreases with f; Xl = 2πfL increases with f.
  • Energy storage: capacitor stores energy in electric field (E = 1/2 C V^2); inductor stores energy in magnetic field (E = 1/2 L I^2).
A past-style question: What is resonance in an RLC circuit? Give the resonant frequency and what happens to impedance/current at resonance.
  • Resonance when inductive and capacitive reactances are equal: Xl = Xc.
  • Resonant frequency: f0 = 1/(2π√(LC)).
  • Series RLC at resonance: impedance minimal (≈ R), current maximal; circuit becomes purely resistive (phase angle ~0).
A past-style question: Explain how a defibrillator uses a capacitor. Include the energy equation and what determines delivered current.
  • Defibrillator charges a capacitor to high voltage, then discharges through the patient via switching circuitry.
  • Stored energy: E = 1/2 C V^2 (so for a given C, energy rises with square of voltage).
  • Delivered current depends on patient impedance and waveform shaping; time constants (effective R and C) influence peak current and pulse duration.
A past-style question: What is capacitive coupling? Give an operating theatre example and methods to reduce it.
  • Capacitive coupling: transfer of AC energy via an electric field between conductors separated by insulation (acts like a capacitor).
  • Example: diathermy cable coupling into ECG leads or other monitoring cables causing artefact or unintended heating/burn risk.
  • Reduction: increase separation, avoid long parallel runs, use shielding, keep cables short, route diathermy leads away from monitoring leads.
A past-style question: What is inductive coupling? Why does twisting a pair of wires help?
  • Inductive coupling: changing magnetic field from a current induces a voltage in a nearby loop (mutual inductance).
  • Twisting reduces loop area and causes induced voltages to alternate in sign along the length, tending to cancel (reduces net pickup).
Calculation-style viva: A 10 µF capacitor is charged to 1000 V. How much energy is stored?
  • Use E = 1/2 C V^2.
  • C = 10 µF = 10 × 10^−6 F; V = 1000 V.
  • E = 0.5 × 10 × 10^−6 × (10^3)^2 = 0.5 × 10 × 10^−6 × 10^6 = 5 J.
Calculation-style viva: What is the capacitive reactance of 1 µF at 50 Hz (mains frequency)?
  • Xc = 1/(2πfC).
  • Xc = 1/(2π × 50 × 1×10^−6) ≈ 1/(3.14×10^−4) ≈ 3.2 kΩ.
Calculation-style viva: An inductor of 0.1 H is in series with a 10 Ω resistor. What is the RL time constant and what does it mean?
  • τ = L/R = 0.1/10 = 0.01 s = 10 ms.
  • After 10 ms, current has risen to ~63% of its final value following a step voltage (or decayed to 37% after switch-off).

0 comments