# Electrical Systems

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

## Variables

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

## Elements

### Capacitors

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

Energy stored:

### Inductors

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

Energy Stored:

### Resistors

• 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

## Example

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

• Resistor:
• Capacitor:
• Inductor:

KVL - the voltages round the loop sum to zero:

Using the capacitor equation, and the fact that :