4

# How can three resistors of resistances 2 , 3 , and 6 be connected to give a total resistance of(a) 4 , and (b) 1 ?

(a) In order to obtain a total resistance of 4 from three resistors of 2 , 3 and 6 .

Firstly, connect the two resistors of 3 and 6 in parallel to get a total resistance of 2 which is less than the lowest individual resistance.  (ii) Then the net R from parallel connection is connected in series with the remaining 2 Q resistor to get a total resistance of 4 Q. This is because in series combination:

R = R1+ R2

R = 2 + 2

R = 4 The arrangement of three resistors of 2,3 and 6 which gives a total resistance of 4 can now be represented as follows : Thus, we can obtain a total resistance of 4 by connecting parallel combination of 3 and 6 resistors in series with 2 resistor.

(b) In order to obtain a total resistance of 1 from three resistors of 2 , 3 and 6Q, all the three resistors should be connected in parallel. This is because in parallel combination:  4
1
Next Question
5

What is (a) the highest, and (b) the lowest, total resistance that can be secured by the combination of four coils of resistances 4 , 8 , 12 and 24 ?