Question

(a) Given n resistors each of resistance R, how will you combine them to get the 

(i) maximum 

(ii) minimum effective resistance? What is the ratio of the maximum to minimum resistance? 

(b) Given the resistances of 1Ω, 2Ω, 3Ω, how will combine them to get an equivalent resistance of 

(i) (11/3)Ω 

(ii) (11/5)Ω 

(iii) 6Ω

(iv) (6/11)Ω 

(c) Determine the equivalent resistance of networks shown in Figure.

Answer 1

(a) (i) The resistance will be maximum when resistors are connected in series. Therefore, maximum resistance.
\(R_{max}\) = R + R + R + ……… n times = nR

(ii) The resistance will be minimum when resistors are connected in parallel. Therefore, minimum resistance,

b. (i) In order to obtain an equivalent resistance of 11/3 Ω the parallel combination of 1Ω and 2 Ω resistances should be connected in series to 3 Cl

(ii) In order to obtain an equivalent resistance of 11/5 Ω, the parallel combination of 2Ω and 3 Ω resistances should be connected in series to, 1 Ω resistance.

(iii) In order to obtain an equivalent resistance of 6Ω, this resistances should be connected in series.

(iv) In order to obtain an equivalent resistance of these resistance should be connected in parallel.

(c) (i)

If battery is connected across the points A and B, then the resistors are in series and hence the equivalent resistance will be the sum of all resistances,
i.e. \(R_{eq}\) = R + R + R + R + R