The purpose of this experiment is to see how passive components impact basic electrical circuits. Passive components do not require an energy source to function. Therefore, they do not generate energy but instead they store or dissipate it. Examples of passive components used in this experiment are resistors, capacitors, inductors, diodes, and switches.

Resistors are electrical components which limit the flow of electrons through a circuit. A resistor follows Ohm’s Law and has the following current-voltage relationship,

V(t)=i(t)*R

where V(t) is the voltage across the resistor measured in units of volts V, i(t) is the current across the resistor measured in units of amperes A, and R is the resistance of the component measured in Ohms ?.

Capacitors are electrical components which store energy in their electrical fields. A capacitor has the following current-voltage relationship,

V(t)=V(to)+1Ct0ti(?)d?

where V(t) is the voltage across the capacitor measured in units of volts V, V(t0) is the initial voltage across the capacitor at time t=0, C is the capacitance of the capacitor measured in Farads F, and i(?) is the current across the capacitor at some time function ?.

Inductors are electrical components which store energy in their magnetic fields. An inductor has the following current-voltage relationship,

V(t)=L*di(t)dt

where V(t) is the voltage across the inductor measured in units of volts V, L is the inductance of an inductor measured in Henrys H, and di(t)dtis the instantaneous current rate of current charge across a inductor.

Diodes are electrical components that allow current to flow through them in only one direction. Every diode has two terminals. One is called an anode (positive end) and the other is a cathode (negative end). Current flows from the anode end to cathode end only.

Switches are electrical components that interrupt current flow in a circuit. There are two states that a switch can be in. One is open which will prevent current from flowing throughout a circuit and the other is closed which will allow current to flow throughout a circuit.

Two theories that were tested during this experiment were Kirchhoff’s current law, KCL, and Kirchhoff’s voltage law, KVL. Kirchhoff’s current law states that the sum of all currents entering and leaving a node must be equal to zero. One can express the relationship as,

ientering-ileaving=0

Kirchhoff’s voltage law states that the sum of all voltages in a loop must be equal to zero. One can express the relationship as,

V14=V12+V23+V34

KCL and KVL were tested on two simple circuits. The first circuit was a voltage divider circuit as seen in Figure 1a and 7. A voltage divider circuit consists of a voltage source and a series of resistors. One can calculate the voltage across a resistor in a voltage divider circuit using,

V12(t)=R1R1+R2Vs(t)or V23(t)=R2R1+R2Vs(t)

depending on which voltage we want to measure. The voltage divider equation states that the voltage across a resistor is directly proportional to the input voltage and the ratio between the two resistors.

The second circuit was a current divider circuit as seen in Figure 1b and 11. A current divider circuit consists of a voltage source and a set of parallel resistors. One can calculate the current across a resistor in a current divider circuit using,

i1(t)=R2R1+R2i(t)or i2(t)=R1R1+R2i(t)

depending on which current shall be measured. The current divider equation states that the current across a resistor is inversely proportional to the total current in the system and the ratio between the two resistors.