T4 - Capacitors and Inductors

Capacitor

Device that stores charge and energy, comprised of 2 closely spaces parallel plates

Equal and opposite charges flow onto places

Effect of applying a potential difference over capacitor

Farads, F

Units for Capacitance, C

Capacitor at DC

Behaves like an open circuit

Ideal Capacitor

Charge remains indefinitely

Instantanenous change in voltage impossible

Condition for capacitor

RC Circuit

Contains a resistor and capacitor only

RC Circuit Properties

Capacitor will discharge, v_c decreases, and resistor absorbs energy

Tau = RC

Time constant in an RC circuit

63%

Capacitor voltage decay after tau seconds in RC circuit

Capacitors in Parallel

C_eq = C₁ + C₂ + C₃

Capacitors in Series

C_eq = 1/(C₁^-1 + C₂^-1 + C₃^-1)

Inductor

Device that produces a magnetic field around the wire when current passes through

Magnetic Flux Density

Proportional to current and number of turns (N)

Flux Density Changes

Potential difference is induced at terminals

Henries, H

Unit for Inductance, L

Inductor at DC

Behaves like a short circuit

Constant Current through Inductor

No induced potential difference, v(t)=0

Instantaneous change in current impossible

Condition for inductor

Energy Stored in Magnetic Field

Dependent on current and inductance, E(t) = ½Li²(t)

Current Increases

Energy in inductor is being stored

Current Decreases

Energy in inductor is being released

RL Circuit

Contains an inductor and resistor only

RL Circuit Properties

Current decreases as inductor’s magnetic field collapses, energy stored in inductor is transferred to resistor

Switch opened in circuit with inductor

Current drops quickly, voltage across switch is large and negative which causes arcing

Tau = L/R

Time constant for RL circuit

63%

Inductor current decay after tau seconds in RL circuit