CBSE Class 10 Science 2018 · Paper 31/1 · Question 12(a)

Electricity 3 marks Medium

Show how would you join three resistors, each of resistance

9 Ω

so that the equivalent resistance of the combination is

Answer

A parallel pair in series with the third resistor gives $13.5 Ω$ ; a series pair in parallel with the third gives $6 Ω$ .

(i) For

13.5 Ω

: connect two of the

9 Ω

resistors in parallel, and connect the third resistor in series with this parallel pair. Then

\frac{1}{R _{p}} = \frac{1}{9} + \frac{1}{9} = \frac{2}{9}

, so

R_{p} = 4.5 Ω

, and

R = 9 Ω + 4.5 Ω = 13.5 Ω

. (ii) For

6 Ω

: connect two of the resistors in series, and connect the third resistor in parallel with this series pair. Then

R_{s} = 9 Ω + 9 Ω = 18 Ω

, and

\frac{1}{R} = \frac{1}{18} + \frac{1}{9} = \frac{3}{18}

, so

R = 6 Ω

. The two arrangements are drawn in the figure.

🔒 Step-by-step solution