Finding Voltage and Current Using Ohm's Law

There is a simple relationship between current, voltage and resistance. This relationship is called Ohm’s Law. The formula is the following.

Difference in Voltage = Current * Resistance

or DV = I * R

This is Form 1 of Ohm's Law.

To find current and resistance the following forms can be used. They are the same as the above formula but in a different form.

Form 2: Current = Difference in Voltage / Resistance

or I = DV / R

Form 3: Resistance = Difference in Voltage / Current

or R = DV / I

These formulas are always used for situations where there are two points with a resistor between them. DV is the difference in voltage between the two points and current is what flows between the two points. These simple relationships allow us to calculate many things. Given any two of the three values (Current, Resistance, and Difference in Voltage) the third can be found. The most common calculation is for current. Voltage is easy to measure and the resistance can be found from the resistor (see color codes). Once these values are known, current can be calculated using Form 2 of Ohm’s law, I = DV / R. For example, consider the problem shown in Figure 1. One side is at 0 volts (ground) and the other side is at 5 volts (with a multimeter, black probe on right side, red probe on left side).

Figure 1

The voltage difference between Point A and Point B is 5 - 0 = 5 volts (DV=5). There is a resistor between the two points which has a value of 500 ohms (R=500). We know that current flows from a point of high voltage to a point of low voltage so we can draw an arrow from the higher voltage to the lower voltage.

Figure 2

Now we can find the current flowing through the resistor using Form 2 of Ohm's Law.

I = DV / R

DV / R = 5 / 500

5 / 500 = 0.01 Amps

0.01 Amps = 10 milliAmps

10 milliamps can be abbreviated as 10 mA

This means the current is 10 mA. ( I = 10mA )

Now to check our answer we can use Form 1 and Form 3 of Ohm’s law. We have to use the value of current in Amps for these formulas. So if we have I = 0.01 Amps and Resistance = 500 ohms then by using Form 1 of Ohm’s law we can find:

Difference in Voltage = DV

DV = I * R

I * R = 0.01 * 500

0.01 * 500 = 5 volts

This is the voltage we started with so the value we found for the current must be right.

We can also check the answer with Form 3 by using I = 0.01 Amps and DV = 5 volts.

Resistance = R

R = DV / I

DV / I = 5 / 0.01

5 / 0.01 = 500 ohms.

So R = 500 ohms

Now consider the problem shown in Figure 3. The voltage on one side is 10 volts and the voltage on the other side is 3 volts. Therefore the voltage difference between the two points is 10 - 3 = 7 volts (DV = 7 V). The resistor is 400 ohms (R = 400).

Figure 3

Then the current flowing from left to right is

I = DV / R

DV / R = 7 / 400

7 / 400 = 0.0175 Amps

0.0175 Amps = 17.5 milliAmps

17.5 milliAmps = 17.5 mA

This means the current flowing from the left to the right is 17.5 mA.

Now suppose we have two points with a voltage difference of 5 volts. Point A is at 5 volts and Point B is at 0 volts (ground). (Notice that the voltage difference is the important part. If Point A is at 7 volts and Point B is at 2 volts then the voltage difference is the same, 7 - 2 = 5 volts.) Now suppose we want a current to flow between Points A and B and we want the current to be 0.02 Amps ( I = 0.02 Amps = 20 mA).

Now we need to find the value of the resistor so we use Form 3 of Ohm’s Law.

Resistance = Difference in Voltage / Current or R = DV / I

DV / I = 5 / 0.02 = 250 ohms

This means that putting a resistor with a value of 250 ohms between Points A and B will make a current flow from Point A to Point B and the current will be 0.02 Amps (20 mA). Now using the values of voltage and resistance, check the value of the current using Form 2 of Ohm’s law.

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