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 = R_{1}+ R_{2}

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 4by 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

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?

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