COMPUTE RESISTOR VALUE
Determine the value to assign to resistor R3 in order to obtain a current equal to 1 Ampere in resistor R1.
SOLUTION
All the needed operations are described in the following figure:
Details here:
We denote by A and B the nodes to which the current generator is connected.
We also denote by I_R1 the current flowing in R1.
We know that this current is equal to 1 Ampere.
Let us now calculate the current I_R2 which flows in R2.
For this purpose, we use Kirchhoff’s law of currents by imposing that the sum of the currents entering node A is equal to that of the currents leaving the same node:
From which:
We now calculate the voltage at nodes A and B by applying Ohm’s law to resistor R1.
Now let’s calculate the resistance that must be present overall to the right of nodes A and B. In the figure it is indicated with RTOT and with orange arrows.
This resistance is obtained by applying Ohm’s law considering that at the ends of the RTOT we have a voltage equal to VAB and the current that crosses the RTOT is equal to IR2.
We therefore have that:
We now observe that RTOT is obtained from the combination of R2, R3 and R4. In particular, R3 and R4 are connected in parallel and as a whole they are then connected in series to R2.
Therefore:
We can now calculate when the resistance given by the parallel connection between R3 and R4 must be valid:
The formula that calculates the resistance of a parallel connection is given by:
By inverting it, we can finally calculate the value of R3:
We can therefore conclude that R3 must be equal to 200 Ohm.
