Current Dividers
If the total current into a set of parallel resistors is known, there is an easy way to determine the current through any individual resistor in the parallel combination. The appropriate formula is called the current divider formula, since the total current is divided among the individual resistors.
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Linear Regression Using Microsoft® Excel™
In this exercise, we will assume a basic familiarity with Microsoft® Excel™. We will briefly present the use of Excel to perform linear regression, or fitting a straight line to a set of data.
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Linear Regression Using MATLAB®
In this exercise, we will briefly present the use of MATLAB® to perform linear regression, or fitting a straight line to a set of data.
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How to Identify a Series
Series circuit elements share the same current. Elements in series can be recognized in two ways: If two and only two elements are connected to a single node, the elements are in series. If applying KCL at a node results in the conclusion that the currents in two elements are identical, the elements are in series.
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Equivalent Resistance
Circuits which consist of resistors connected in parallel can be simplified. This topic page will explain how.
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Voltage Dividers
If the total voltage difference across a set of series resistors is known, there is an easy way to determine the voltage across any individual resistor in the series combination. The appropriate formula is called the voltage divider formula, since the total voltage is divided among the individual resistors.
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Equivalent Resistance
When resistors are connected in series, a simplification of the circuit is possible.
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Voltage-Current Characteristics and Nonlinearities
In this section, we will look at Ohm's law from the standpoint of a voltage-current relationship. This will provide some continuity with our presentation of voltage current relationships for other components, such as capacitors, inductors, diodes, and transistors later on.
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Magnetism
Similarly to charges, magnets exert forces on one another over a distance. Each magnet has two poles—a north and a south pole. A magnet's north pole will be attracted to the south pole of another magnet, while the north poles or south poles of two magnets will repel each other.
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Current and Voltage
This topic page covers background material relating to current and voltage.
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Design Challenge 1: Nominal Resistance Variations
In this exercise, we will be measuring the resistance of several resistors that all have the same nominal resistance in order to determine the actual resistor-to-resistor resistance variations.
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Design Challenge 2: Resistance Measurement Variations
We will use some basic statistical analyses in this section to examine measurement variations. Statistics are a way to quantify variations in results which are due to random effects—or minimize the significance of these effects on our final conclusions.
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Design Challenge 3: Choosing Resistance
A common problem in designing electric circuits is having to pick a resistance that provides the desired amount of current. In this project, we will create a circuit (i.e. choose a resistor) which results in a specified current being provided by a 5V source.
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Design Challenge 4: Current-Limiting Resistor
Resistors in electrical circuits are commonly used to provide other components in the circuit with the voltages and currents they require in order to function properly. For example, in this exercise, we will design our circuit (i.e. choose a resistance value) to ensure that an LED receives the voltage necessary for it to light up without allowing excessive current, which could burn out the LED.
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Design Challenge 5: Inferring Current From Voltage
Measuring current directly tends to be tedious—you generally need to break open your circuit in order to insert the ammeter into the circuit. Voltage measurements tend to be considerably easier, so it is common to determine the current in a circuit by measuring the voltage across a known resistor and using Ohm's law to estimate the current through the resistor.
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Adding Series Resistors
In this project, we will expand our understanding of resistors in series by finding three fixed resistors—when combined in series, they will provide a specified resistance.
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Design Challenge 1: Series Resistors
In this design challenge, we will build a circuit with a 5V source, 6.8 kΩ, and an arbitrary resistor. We will use the concept of voltage division to determine the resistance value of the arbitrary resistor when given a specific voltage drop across it.
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Design Challenge 2: Controlling Current
Voltage dividers and resistors in series can also be used to control the amount of current that is drawn from a power source.
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Design Challenge 1: Temperature Measurement
Design a circuit whose output voltage provides a crude temperature measurement.
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Design Challenge 2: Temperature Measurement
Design a circuit so that the output voltage of the system to be zero at room temperature, increase as temperature increases, and decrease as temperature decreases.
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Power Limitations
Design a resistive network to draw a relatively large amount of power from a source and observe what happens when a resistor fails.
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