In the circuit to the left, there is one voltage source and two resistors. In this example we will calculate different values.
Example 1
Given:
U = 16 V
I = 2 A
R_{1}= 5 Ohm
What is the resistance of resistor R_{2}?
Answer
To calculate the resistance of R_{2}, we need to use Ohm's law and the Kirchhoff's voltage law. Apply Kirchhoff's voltage law and write down the equation for the loop you can see:
U  U_{R1}  U_{R2} = 0
The voltage from the voltage source is added as it is counter clockwise. The voltage of the loads is subtracted as it is clockwise.
Of these three values, we only know U. We do not know U_{R1} and U_{R2}. But for U_{R1} we know both the resistance and the current so we can calculate the voltage by applying Ohms law:
U_{R1} = R_{1} * I
You see, here the second form of Ohm's law is applied. Like this we can calculate the voltage over the resistance R_{1}. We insert the values we are given:
U_{R1} = 5 Ohm * 2 A = 10 V
We know now that the voltage of the resistor R_{1} is 10 V. Now we can use this in the Kirchhoff's voltage law from above.
U  U_{R1}  U_{R2} = 0
16 V  10 V  U_{R2} = 0
6 V  U_{R2} = 0
6 V = U_{R2}
We have calcualted the voltage over resistor R_{2}. The next step is to calculate the resistnace of R_{2}. For thism we again use the Ohm's voltage law.
Have a look at the note above. You can see that the last form of Ohm's law says that resistance is voltage over current. So to calculate the resitance of R_{2}, we need to know the current flowing through the resistor and we need to know the voltage over the resistor.
R_{2} = U_{R2} / I
R_{2} = ^{6 V}/_{2 A}
R_{2} = 3 ^{V}/_{A} = 3 Ohm
The solution to this problem was quite long. The important thing is to know what you need, and then find a way to the solution. Often this requires more than just one step.
In the example here, we needed to know the resistance of a certain resistor. So going backwards, we see that we could calculate this resistance, if we have the current and the voltage over this resistance. But we did not have the voltage. So we found a way to calculate the resistance. With Kirchhoff's second rule, we know that if we know the voltage U and the voltage at resistor R_{1}, then we could calculate the voltage of the other resistor. But we didn't have the voltage over R_{1}. To obtain this voltage we again needed Ohm's law using the resistance R_{1} and the current I. Once we have calculated the voltage over R_{1} we can calcualte the voltage over R_{2}. Then when we know this voltage we can calculate the resistance using Ohm's law.
