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Engineering LibreTexts

2.1.9: Summary

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  • Electrons are the charge carrier in metals. Their direction of travel, called electron flow, runs from the negative terminal of a voltage source to the positive terminal. The more commonly used conventional current flow runs from the positive terminal to the negative terminal. As conventional current enters a resistor, we mark this point as positive, and where it exits, negative. Thus, any voltage with a + to − polarity is deemed a voltage drop (which dissipates energy in a resistor). A polarity of − to + is deemed a voltage rise.

    A series connection is any connection in which the current through one component must be identical to the current flowing through any other component in that connection. In other words, the current exiting any component must be the only current flowing into the next component in line; there can no intervening connections for current flow to or from other parts of the circuit. The equivalent resistance of a string of resistors placed in series is simply the sum of their resistance values. Consequently, the larger resistors dominate the equivalent value.

    Ohm's law states that the voltage across a resistor must equal the product of its resistance and the current flowing through it.

    Kirchhoff's voltage law (KVL) states that the sum of voltage rises around any series loop must equal the sum of voltage drops around that loop. Alternately, it may be stated as the sum of voltage rises and drops around a series loop must be zero, as the rises and drops have opposite polarity.

    The voltage divider rule (VDR) is a convenient computational shortcut based on Ohm's law and KVL. It states that the voltage across any given resistor or group of resistors in a series connection is proportional to their resistance as a percentage of the total resistance. For example, if a resistor makes up one quarter of the total resistance in a series string of resistors, then that resistor will get one quarter of the total voltage applied to that string.

    A potentiometer, or pot, is a three terminal variable resistance. The resistance of the entire device is fixed, however, a third lead is attached internally to an adjustable wiper, effectively creating two resistors. The sum of the two parts always equals the nominal value of the pot with the values of each piece being determined by the position of the wiper. Pots may be either rotary or linear (straight line) in motion and are used typically to adjust a voltage level. If the wiper and only one of the end terminals is used, the device is called a rheostat. A common application for a rheostat is the control of current.

    Finally, computer simulation tools may be used to build virtual circuits and determine various parameters such as voltages and currents. They may use virtual instruments that echo real world instruments or they may use more direct means, offering results in the form of tables.

    Review Questions

    1. Describe the differences between electron flow and conventional current flow.

    2. Define the term series connection.

    3. How is the equivalent resistance for a string of series connected resistors computed? Is the process identical for series connected voltage sources?

    4. Why are current sources generally not placed in series?

    5. Define Ohm's law.

    6. Define Kirchhoff's voltage law.

    7. Define the voltage divider rule.

    8. What is meant by a Monte Carlo analysis?

    9. What is the difference between a potentiometer and a rheostat?

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