Designing Animated Simulations and Web-Based Assessments to Improve Electrical Engineering Education - Web-Based Engineering Education: Critical Design and Effective Tools - page 80

Table 2. AC & DC circuit invariants list

Invariant Description

For resistors, capacitors, and inductors the current through the component is directly proportional to the voltage
across the component. The ratio of voltage drop to current is the impedance of the component.
For a resistor, the impedance is the resistance value, R. For capacitors (and inductors) the impedance is a function
of the capacitance (or inductance) and the frequency of voltage and current.

a. Ohm's Law

The impedance of a capacitor is inversely related to the capacitance value and the frequency of the source.
(Specifically the impedance of a capacitor is given by the expression: X C = 1/(2*pi*f*C), where f is the frequency,
and C is the capacitance).

b. Impedance of a
Capacitor

The charge held by a capacitor is directly proportional to the value of capacitance, C, and the voltage drop across
it. (Q = C*V). Another way to express this relation is I = C * dV/dt, i.e., the current through a capacitor is related to
the rate of change of the voltage across the capacitor.

c. Charge held by
a Capacitor

The impedance of an inductor is directly related to the inductance value and the frequency of the source. (Specifi-
cally the impedance of an inductor is given by the expression: X L = 2*pi*f*L, where f is the frequency, and L the
impedance.)

d. Impedance of an
Inductor

The flux held by an inductor is directly proportional to the value of inductance, L, and the current through it.
Another way to express this relation is V = L * dI/dt, i.e., the voltage drop across an inductor is related to the rate
of change of current through the inductor.

e. Inductor and
Flux

To determine the power dissipated by a resistor one has to know at least two of the three quantities for the resis-
tor: its resistance, the voltage drop across the resistance, and the current through it. (Mathematically the power
consumed = V*I = V 2 /R = I 2 *R)

f. Power

Kirchoff's Voltage Law (KVL):
Consider a closed loop consisting of one or more components. KVL states that the voltage drops across all ele-
ments in the loop at any instant of time must sum to zero. This relation holds universally for any set of components,
and is independent of the frequency of the voltage and current.
Kirchoff¹s Current Law (KCL):
KCL states that the sum of the magnitudes of currents flowing into a point where a number of components are con-
nected together must equal 0. (Current flowing away from the point is given a negative value). This relation holds
universally at any point in time, and is not dependent on the frequency of the voltage and current.

g. Kirchoff's Laws
of Conservation

(a) Resistances in Series:
The effective resistance of a set of resistances connected in series is the sum of the individual resistances. So in a
series combination, the effective resistance always increases.
(b) Resistances in Parallel:
The effective resistance of a set of resistances connected in parallel is given by the formula: 1/R effective = 1/R1 + 1/
R2 + ...
In a parallel combination, the effective resistance is always smaller.

h. Effective resis-
tance

Figure 1. Range of circuit misconceptions seen on misconceptions test