Electrical Systems

Similar to mechanical systems, models of electrical systems can be constructed. Similar deal to ES191.


  • Current in amps (A)
  • Voltage in volts (V) -- not v for voltage, e is used in systems
  • Power in watts



  • Store electrical energy in a reversible form
  • Capacitance measured in Farads (L)

Elemental equation:

Energy stored:


  • Store magnetic energy in a reversible form
  • Inductance measured in Henries (H)

Elemental equation:

Energy Stored:


  • Dissapates energy
    • Non-reversible
  • Resistance measured in Ohms ()

Elemental Equation (Ohm's law):

Voltage Source

  • Provides an input of energy to the system.
  • Input voltage

Kirchhoff's Laws

  • Describe how elements interconnect and transfer energy between them
  • KVL - voltages around a closed loop sum to zero
  • KCL - currents about a node sum to zero


Form a differential equation to model the following electrical system/circuit:


  • Resistor:
  • Capacitor:
  • Inductor:

KVL - the voltages round the loop sum to zero:

Using the capacitor equation, and the fact that :