Ohm’s Law
8–1 VOLTAGE, CURRENT, AND RESISTANCE
The three quantities E, I, and R relate to one another in a very significant way. This relationship, first formulated by the German scientist Georg S. Ohm, states that the current (I) is directly proportional to the voltage (E) but inversely proportional to the resistance (R). In other words,
This equation is known as Ohm’s law and can be algebraically transposed and rewritten into other forms, namely,
Ohm’s law is one of the most important formulas in electrical theory. It enables us to compute unknown circuit quantities, thereby helping us to predict or confirm proper
circuit operation. Memorize Ohm’s law, because you will encounter it time and again in your future studies of electricity and electronics.
A popular memory device, for some students, has Ohm’s law arranged in a circle, as shown in Figure 8–1. To use this circle, place a finger on the letter representing the unknown quantity. The other two letters will show themselves in the proper arrangement to indicate either multiplication or division.
EXAMPLE 8–1
Given: A resistance (R) of 4 ohms connected to a 12-volt battery (E).
Find: The current (I).
Solution
Covering the letter I in the memory circle suggests the correct formula:
EXAMPLE 8–2
Given: A current (I) of 6 amperes flowing through a 4-ohm resistance (R). Find: The voltage (E) needed to force the current through the resistance.
Solution
Wanting to find the voltage (E), cover the letter E within the memory circle. This would suggest that
EXAMPLE 8–3
Given: A source of 6 volts (E) forcing a current of 1.5 amperes (I) through a resistor (R). Find: The value of the unknown resistor.
Placing your finger on the unknown value (R) of your memory circle will suggest that
8–2 OHM’S LAW WITH METRIC PREFIXES
Ohm’s law is designed for use with basic units only. That means:
• Current must be expressed in amperes.
• Voltage must be expressed in volts.
• Resistance must be expressed in ohms.
Special precaution must be observed when given values are stated with metric pre- fixes instead of basic units. In such cases it is recommended to convert the metric prefixes to powers of 10.
EXAMPLE 8–4
Given: An electromotive force of 100 volts and a current of 20 milliamperes.
Find: The resistance.
Solution
EXAMPLE 8–5
Given: A 3-kilohm resistor is connected to a 12-volt power source.
Find: The current.
Solution
EXAMPLE 8–6
Given: A current of 2 milliamperes is flowing through a 5-kilohm resistance.
Find: The voltage.
SUMMARY
• Ohm’s law states that:
1. Current and voltage are directly proportional.
2. Current and resistance are inversely proportional.
• Mathematically, Ohm’s law may be expressed by the equations
• When solving Ohm’s law problems, numerical values must be stated in basic units (volts, amperes, and ohms).
Achievement Review
1. Given voltage = 120 volts and current = 4 amperes, find resistance.
2. Given resistance = 6 ohms and current = 3 amperes, find voltage.
3. Given voltage = 24 volts and resistance = 8 ohms, find current.
4. Given voltage = 150 volts and resistance = 450 ohms, find current.
5. Given current = 5.5 amperes and voltage = 440 volts, find resistance.
6. Given voltage = 6 volts and resistance = 0.05 ohms, find current.
7. Given current = 0.022 ampere and voltage = 660 volts, find resistance.
8. Given voltage = 60 volts and current = 0.01 ampere, find resistance.
9. Given resistance = 48 ohms and current = 2.5 amperes, find voltage.
10. Given voltage = 12 volts and current = 0.002 ampere, find resistance.
11. Given resistance = 50,000 ohms and voltage = 250 volts, find current.
12. Given current = 0.01 ampere and resistance = 3,000 ohms, find voltage.
13. Given resistance = 7.5 ohms and current = 4.5 amperes, find voltage.
14. Given resistance = 31.4 ohms and current = 3.99 amperes, find voltage.
15. Given resistance = 480 ohms and current = 220 milliamps, find voltage.
16. Given current = 50 milliamps and resistance = 2 kilohms, find voltage.
17. Given resistance = 30,000 ohms and current = 3 milliamps, find voltage.
18. Given voltage = 100 volts and resistance = 10 kilohms, find current.
19. Given voltage = 240 volts and current = 8 milliamps, find resistance.
Given current = 0.002 ampere and voltage = 6.62 volts, find resistanc