2.7 Resistors and Ohm’s Law
Resistor. Resistors are circuit elements designed to impede the flow of current by absorbing energy and, hence, decreasing voltage across their terminals. They are used in circuits to limit current, to divide voltages into fractional parts, to “pull up” and “pull down” input values (to be discussed in a subsequent chapter), to establish timing in conjunction with capacitors and other applications. A resistor has a voltage drop, or voltage decrease, across its terminals proportional to the current flowing between the terminals. Ohm’s law stipulates that the voltage drop across and current through a resistor are related by
(1)
or, by trivial algebraic manipulation,
(2)
where is the resistance having units of or Ohms, .
This current vs. voltage relationship (also referred to as an relationship) defined by equations (1) and (2) can be plotted on and axes as shown. The linear relationship between current and voltage holds for all values of and , meaning that resistor is a linear circuit element.
Note that for a resistor, the voltage drops, or decreases, in the direction of positive current flow; that is, positive charges, when moving through a resistor in the direction of the voltage drop, are giving up energy. The energy gets converted to heat in the resistor at a rate of
(3)
which is the power absorbed by the resistor, in Watts. Equation (5) can be re-written, using equations (1) and (2)
(4)
and
(5)
which are two additional equations for determining the power absorbed by a resistor.
Examples
Determine voltage drop and the power dissipated in the resistor in the circuit shown in Figure 2.60
Solution: Ohm’s law specifies that volt.
The power dissipated in the resistor is watt.
Determine the voltage drop across the resistor shown
Solution: Here, we need to pay attention to the direction of the current relative to the voltage drop. Ohm’s law specifies that when the current, , enters the positive polarity of the voltage drop, . In this problem, the voltage drop will be in the direction of the current. In other words, the voltage drop will have its positive polarity where the current enters the resistor. Therefore, .
Determine the voltage drop across the resistor in the circuit shown when the AC current given by
Solution: Ohm’s law is valid for DC, AC, and combined AC and DC waveforms. In this case,
Note that in the these example problems, upper case variables were used for DC voltages and currents, whole lower-case variables were used for AC voltages and currents. Note also that the time dependence for AC variables is often suppressed when drawing circuits.
Resistor values. Resistors are manufactured with standard resistance values from 1Ω to 10M Ω and they can readily purchased with tolerance values of 10%, 5%, and 1%. Different tolerance values can be purchased along with different power-handling capacities. Resistors have color bands on them that allow their resistance value to be determined via color code charts such as th