Voltage Calculations

The second application of Ohm’s Law is to find unknown dc voltages when the current and the resistance are known. Let’s work out some problems of this kind.

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A circuit for working Ohm’s Law problems

Problem 1

Suppose the potentiometer in above figure is set to 100 Ω, and the measured current is 10 mA. What is the dc voltage?
Use the formula E = IR. First, convert the current to amperes: 10 mA = 0.01 A. Then multiply: E = 0.01 × 100 = 1.0 V. That’s a little less than the voltage produced by a flashlight cell.

Problem 2

Adjust the potentiometer in above figure to a value of 157 kΩ, and suppose the current reading is 17.0 mA. What is the voltage of the source?
You must convert both the resistance and the current values to their proper units. A resistance of 157 kΩ is 157,000 Ω, and a current of 17.0 mA is 0.0170 A. Then E = IR = 0.017 × 157,000 = 2669 V = 2.669 kV. You should round this off to 2.67 kV. This is a dangerously high voltage.

Problem 3

Suppose you set the potentiometer in above figure so that the meter reads 1.445 A, and you observe that the potentiometer scale shows 99 Ω. What is the voltage?
These units are both in their proper form. Therefore, you can plug them right in and use your calculator: E = IR = 1.445 × 99 = 143.055 V. This can and should be rounded off—but to what extent? This is a good time to state an important rule that should be followed in all technical calculations.

The Rule of Significant Figures

Competent engineers and scientists go by the rule of significant figures, also called the rule of significant digits. After completing a calculation, you should always round the answer off to the least number of digits given in the input data numbers.

If you follow this rule in Problem 3, you must round off the answer to two significant digits, getting 140 V, because the resistance (99 Ω) is only specified to that level of accuracy. If the resistance were given as 99.0 Ω, then you would round off the answer to 143 V. If the resistance were given as 99.00 Ω, then you could state the answer as 143.1 V. However, any further precision in the resistance value would not entitle you to go to any more digits in your answer, unless the current were specified to more than four significant figures.

This rule takes some getting used to if you haven’t known about it or practiced it before. But after a while, it will become a habit.