Find the equivalent resistance of the network shown in figure between points A and B.

where k is a positive constant.

Explanation

The given network can be redrawn as shown.
Here, `(P)/(R)=(kr)/(k^(2)r)=(1)/(k)`
`(Q)/(S)=(r )/(kr)=(1)/(k)`

This is a case of balanced Wheatstone bridge.No current flow through CD fi poitns A and B connected to two terminals of a battery . So, resistance kr and `k^(2) r` are in series and resistance `(r )/(k)` and r are in series.
Network can also be drawn in the diagram here. Thus, equivalent resistance between points A and B is.
`R_(AB)= (kr(k+1)(r )/(k) (k+1))/(kr(k+1)+(r )/(k)(k+1))`
`= (kr(k+1))/((k^(2)+1))`