Page 91 - Teach Yourself Electricity and Electronics

Resistance calculations 71

you can do about it unless you are willing to use units of nanoamperes (nA), or bil-
lionths of an ampere. Then you can say that the current is 186 nA.

Voltage calculations

The second use of Ohm’s Law is to find unknown voltages when the current and the re-
sistance are known. For the following problems, uncover the ammeter and cover the
voltmeter scale instead in your mind.
Problem 4-4
Suppose the potentiometer (Fig. 4-7) is set to 100 ohms, and the measured current is
10 mA. What is the dc voltage?
Use the formula E I R. First, convert the current to amperes: 10 mA = 0. 01 A.
Then multiply: E 0. 01 100 1 V. That’s a low, safe voltage, a little less than what
is produced by a flashlight cell.

Problem 4-5
Adjust the potentiometer (Fig. 4-7) to a value of 157 K , and let the current reading be
17 mA. What is the voltage of the source?
Now you have to convert both the resistance and the current values to their proper
units. A resistance of 157 K is 157,000 ; a current of 17 mA is 0. 017 A. Then E IR
0.017 157,000 2669 V 2.669 kV. You might want to round this off to 2.67 kV.
This is a dangerous voltage. If you touch the terminals you’ll get clobbered.
Problem 4-6
You set the potentiometer (Fig. 4-7) so that the meter reads 1.445 A, and you observe
that the potentiometer scale shows 99 ohms. 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 to 143 V. A purist would go further and round it to the nearest 10 volts, to
140 V.
It’s never a good idea to specify your answer to a problem with more significant fig-
ures than you’re given. The best engineers and scientists go by the rule of significant
figures: keep to the least number of digits given in the data. If you follow this rule in
Problem 4-6, you must round off the answer to two significant figures, getting 140 V, be-
cause the resistance specified (99 ) is only accurate to two digits.

Resistance calculations

Ohms’ Law can be used to find a resistance between two points in a dc circuit, when the
voltage and the current are known. For the following problems, imagine that both the
voltmeter and ammeter scales in Fig. 4-7 are visible, but that the potentiometer is un-
calibrated.