Rahul went to an electronics shop to get his father's old radio set repaired. The radio mechanic required resistances of 1.5 Omega and 10 Omega to repair the radio set properly but he had only a large number of 3 Omega resistors. The radio mechanic made many attempts but could not get the right combinations of 3 Omega resistors to obtain 1.5 Omega and 10 Omega resistances. Rahul had studied combination of resistors in class X. Rahul thought for a while and then joined some 3 Omega resistors in two different ways to obtain the required resistances. (a) How did Rahul obtain 1.5 Omega resistance by joining a number of 3 Omega resistors ? (b) How many 3 Omega resistors were combined together to obtain 1.5 Omega resistance ? (c) How did Rahul obtain 10 Omega resistance by joining a number of 3 Omega resistors ? (d) How many 3 Omega resistors were combined together by Rahul to obtain 10 Omega resistance ?
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Answer:
(a) In order to obtain 1.5Ω resistance, Rahul first combined three 3Ω resistors in parallel to obtain a resistance of 1Ω. He then connected six 3Ω resistors in parallel to obtain a resistance of 0.5Ω. These two parallel combinations were then connected in series to obtain a resistance of 1+0.5=1.5Ω (see Figure 1)
(b) Nine 3Ω resistors.
(c) In order to obtain 10Ω resistance, Rahul first connected three 3Ω resistors in parallel to obtain a resistance of 1Ω. He then connected three 3Ω resistors in series to get a resultant resistance of 9Ω. The parallel combination and series combination were then connected in series to obtain a final resistance of 1+9=10Ω (see Figure 2).
(d) Six 3Ω resistors.
(e) Rahul showed the values of (i) Knowledge of combination of resistors (ii) Application of knowledge, and (iii) Desire ot help others.
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