Whats the equivalent resistance of the following three circu

What\'s the equivalent resistance of the following three circuits?

Solution

We need to keep following points into consideration for solving the given problems:

1.) For resistors in series, the net resistance is equal to the sum of each resistor while for parallel connection, 1 /Rnet = 1 /R1 + 1/R2 + 1/R3 and so on

2.) For any circuit, if we manage to find a path with no resistor in it, the circuit is said to be short and the net resistance in that case is zero.

We will use the above to solve the given problems as:

a.) The circuit here is apparently short, hence the net resistance is zero.

b.) Here R5 and R6 are in parallel, so R₅₆ = 200 x 300 / 500 = 120 Ohms

This combination is in turn in series with R4.

Therfore the net resistance for the circuit would be R4 + R₅₆ = 120 + 100 = 220 Ohms

c.) Here, again, the resistors R8 and R9 are short, hence the net resistance will be equal to that of R7

Therefore Rnet = 100 Ohms

NOTE: Of course it is imperative to identify that the circuits are short or not, the combinations are in parallel or series. Try traversing the circuit from end to end and see how the resistors are laid out. If between any two points you can find multiple paths, those paths are in parallel, however, you need to be careful as those paths themselves have resistors in them in parallel or series. It is always better to break down the circuit in parts and then resolve.