question_answer 20)

(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 1, 2, 3, how will be combine them to get an equivalent resistance of (i) (11/3) , (ii) (11/5), (iii) 6, (iv) (6/ 11 ) ?                 (c) Determine the equivalent resistance of networks shown in figure.                                

Answer:

(a) (i) Maximum resistance can be obtained by combining them in series with each other.                 The maximum resistance Rmax = R + R + R +?? n times = nR.                 (ii) Minimum effective resistance can be obtained by combining them in parallel with each other.                 Minimum resistance Rmin is found as                  times                                                                               (b) Here R1 = 1                 and R3 = 3.                 (i) If we combine R1 and R2 in parallel and R3 in series with them as shoe - then equivalent resistance                                                 (ii) If we combine R2 and R3 in parallel with each other and this combination is connected in series with R1, then the equivalent resistance is                                                   (iii) If R1, R2 and R3 are combined in series, then                 R = R1 + R2 + R3 = 1 + 2 + 3                 = 6.                 (iv) If R1, R2 and R3 are combined in parallel, then                                                                   (c) (i) The network consists of four similar units.                 Resistance of one unit is given by Req                                 Total resistance                    (ii) All the resistors are in series