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Note that current is defined as the flow of positive charges.
v = Ri is Ohm's Law. It's an important equation; commit it to memory.
Click here (Florida State University) to find out how to use the resistor color code.
Mega (106), kilo (103), milli (10-3), micro (10-6), nano(10-9), and pico(10-12) are the most commonly used multipliers. Commit them to memory.
Two elements are in series if they are connected together at one end with no other connection at that end. Use this definition, rather than your intuition, to determine if elements are in series. The following elements are in series:
These elements are not in series:
For resistors in series, the net resistance is just the sum of the individual resistances.
REQ = R1 + R2 + ..... Rn
Two elements are in parallel if both ends of each element are connected together. These elements are in parallel:
These elements are not in parallel:
A parallel combination of resistors is found by the equation
1/REQ = 1/R1 + 1/R2 + 1/R3 + ..... 1/Rn
A useful special case is for exactly two resistors in parallel:
REQ = R1R2/(R1 + R2)
The equations for elements in series and parallel are easily derivable from Kirchhoff's Laws.
Before going on, you should complete Tutorial 2 on resistors in series and parallel.
Some circuits, such as the one shown below, cannot be simplified by combining elements in series and parallel. When this happens, you just have to grit your teeth and apply Kirchhoff's Laws, or use the delta-wye transformation (discussed in a later section).
An open circuit is a place in a circuit where nodes are not connected, or open. Zero amps flows between nodes that are not connected, meaning zero amps flows in an open circuit. The resistance across an open circuit is equal to infinity. Open circuits are represented as a broken wire. For calculating an equivalent resistance, a resistor connected to the circuit at only one node is open. An open resistor (1) makes zero Ohms of contribution to the equivalent resistance and (2) can be removed from the circuit when calculating the equivalent resistance.
Open circuit = 0A of current
Open circuit = ∞Ω of resistance
An element (e.g., resistor, voltage source, etc.) is shorted if both of its ends are connected to the same one node. Short circuits are represented as a wire. A wire is considered to have a negligible amount of voltage, or zero volts, meaning the voltage is zero for a short circuit. The resistance of a wire in electrical circuits is considered to be negligible, or 0Ω. Therefore, the resistance across a short circuit is negligible, and considered equal to zero. For calculating an equivalent resistance, a shorted resistor is one whose both ends are connected to the same one node. A shorted resistor (1) makes zero Ohms of contribution to the equivalent resistance and (2) can be removed from the circuit when calculating the equivalent resistance.
Short circuit = 0V of voltage
Short circuit = 0Ω of resistance
The voltage divider equation will be very useful to you. Consider the figure below.
It is easily derivable from Kirchhoff's Laws that
V2 = VSR2/(R1 + R2)
The current divider equation may be occasionally useful. Consider the figure below.
Similar to the voltage divider equation, Kirchhoff's Laws can be used to find that
I2 = ISR1/(R1 + R2)
Notice that the numerator term uses the resistor that the current doesn't go through.
Before going on to the homework, you should complete Tutorial 2A on voltage and current dividers.
Please note: It is not necessary to use delta-wye transformation in any of these problems.
Bonus (no partial credit). All resistors are 1 Ω. Find an
expression for RGH that can be expanded to as many decimal places as
RGH = (π - 3)/7 (Not the right answer).