Question

Rahul went to an electronics shop to get his father’s old radio set repaired. The radio mechanic required resistances of 1.5 Ω and 10 Ω to repair the radio set properly but he had only a large number of 3 Ω resistors. The radio mechanic made many attempts but could not get the right combinations of 3 resistors to obtain 1.5 Ω and 10 Ω resistances. Rahul had studied the combination of resistors in Class X. Rahul thought for a while and then joined some 3 Ω resistors in two different ways to obtain the required resistances.

1. How did Rahul obtain 1.5 Ω resistance by joining a number of 3 Ω resistors?
2. How many 3 Ω resistors were combined together to obtain 1.5 Ω resistance?
3. How did Rahul obtain 10 Ω resistance by joining a number of 3 Ω resistors?
4. How many 3 Ω resistors were combined together by Rahul to obtain 10 Ω resistance?
5. What values are shown by Rahul in this episode?

Answer 1

(i) Rahul obtained this by connecting the 3 Ω resistors in a parallel combination.

(ii) Two 3 Ω resistors were combined together to obtain a resistance of 1.5 Ω.

Formula:

`1/R_p = 1/3 + 1/3`

`1/R_p = 2/3`

`R_p = 3/2`

R_p = 1.5 Ω

(iii) Rahul made a mixed combination:

1. Connected three 3 Ω resistors in series to get 9 Ω (3 + 3 + 3 = 9 Ω)

2. Connected another three 3 Ω resistors in parallel to get 1 Ω `(1/(1/3 + 1/3 + 1/3) = 1 Ω)`.

3. Then, he joined both groups together in series (9 Ω + 1 Ω = 10 Ω).

(iv) 6 resistors in total (3 in series + 3 in parallel).

(v) Practical application of scientific knowledge, critical thinking, problem-solving skills, and a helpful nature toward others.