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.

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A circuit for working Ohm’s Law problems

Problem 1

If the voltmeter in above figure reads 24 V and the ammeter shows 3.0 A, what is the resistance of the potentiometer?
Use the formula R = E/I, and plug in the values directly, because they are expressed in volts and amperes: R = 24/3.0 = 8.0 Ω. Note that you can specify this value to two significant figures, the 8 and the 0, rather than saying simply 8 Ω. This is because you are given both the voltage and the current to two significant figures. If the ammeter reading had been given as 3 A, you would only be entitled to express the answer as 8 Ω, to one significant digit. The digit 0 can be, and often is, just as important in calculations as any of the other digits 1 through 9.

Problem 2

What is the value of the resistance in above figure if the current is 18 mA and the voltage is 229 mV?
First, convert these values to amperes and volts. This gives I = 0.018 A and E = 0.229 V. Then plug into the equation: R = E/I = 0.229/0.018 = 13 Ω.

Problem 3

Suppose the ammeter in above figure reads 52 μA and the voltmeter indicates 2.33 kV. What is the resistance?
Convert to amperes and volts, getting I = 0.000052 A and E = 2330 V. Then plug into the formula: R = E/I = 2330/0.000052 = 45,000,000 Ω = 45 MΩ.