How do I calculate total resistance?

Question

As far as I understand, two resistors are connected in parallel if the node at both ends of both resistors are the same. And in series if only one node is the same.

But what if between two resistors there is/are some component(s) like Voltage Source, Current Source, Ammeter, etc?

For example in this circuit:

The R2 is parallel to the R3. $$=> R_{23} = R_{2} || R_{3}$$

But after that, the R1 is parallel or in series to R23? And why?

And if there was no current source, would it change the relationship between R1 and R23?

Thanks.

Answer 1

\$R_1\$ is neither parallel nor in series with \$ R_2||R_3 \$. You have to apply KCL and KVL to find the resistance seen by E or J current sources. If there is no current source J and the branch is shorted, then \$R_1\$ would be in parallel with \$ R_2||R_3 \$.

The general rules to decide if two resistors are in parallel or series are:

1. If the potential difference between both ends of each resistor is same,the resistors are in parallel.
2. If same current flows through both resistors, the resistors are in series .

Answer 2

The current source produces a constant currency applied over a constant resistance R23. Sounds like it's actually a voltage source at that point, right? The voltage at the top of R23 must be J * R23 because of Ohms law.