Electrical circuits in industrial instrumentation

Electrical circuits are ubiquitous in industrial instrumentation, and so it is imperative that you master their analysis.

Conservation of Energy

→ Energy cannot be created or destroyed

Conservation of Electric Charge

→ Electric charges cannot be created or destroyed

Properties of a series network

→ Definition: only one path for electric current
→ Current the same through each component (Conservation of Electric Charge)
→ Voltages add to equal the total (Conservation of Energy)
→ Resistances add to equal to total

Properties of a parallel network

→ Definition: each component connected across the same two sets of electrically common points
→ Voltage the same across each component (Conservation of Energy)
→ Currents add to equal the total (Conservation of Electric Charge)
→ Resistances diminish to equal to total

Kirchhoff’s Voltage Law (KVL)

→ A test charge moved from one location to any series of other locations and back to the starting
location must arrive with the same amount of potential energy as it began (Conservation of Energy)

Kirchhoff’s Current Law (KCL)

→ Every charge entering a point must be balanced by a charge exiting that point (Conservation of
Electric Charge)

Ohm’s Law

→ The voltage dropped across a resistance is equal to the product of its resistance and the amount of
current through it: V = IR

Capacitance and Inductance

→ The ability to store energy in and retrieve energy from electric fields and magnetic fields, respectively

→ Current through capacitance is equal to the product of its capacitance and the rate-of-change of voltage across it: I = C dV/dt

→ Voltage across inductance is equal to the product of its inductance and the rate-of-change of current through it: V = LdI/dt