Question

Show how you would connect three resistors, each of resistance 6 Ω, so that the combination has a resistance of (i) 9 Ω, (ii) 4 Ω.

NCERT Class X
Science - Science

Chapter _Electricity

Answer 1

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Answer 2

Given : There are three identical resistors of resistance 6Ω.

To show : how we would connect these three resistors so that the combination has a resistance of (i) 9Ω (ii) 4Ω

solution : (i) see 1st diagram, here two resistors are joined in parallel and one is joined in series with those ones.

if you find effective resistance ;

1/R₁ = 1/6 + 1/6 [ two resistors are in parallel ]

R₁ = 3Ω

now R₁ is joined in series with first 6Ω.

so, effective resistance, R = 3 + 6 = 9Ω.

(ii) see 2nd diagram, here two resistors are joined in series and these two are joined in parallel with third one.

R₁ = 6 + 6 = 12Ω [ two resistors are in series]

now R₁ is joined in parallel with 6Ω.

so, effective resistance, R = 12 × 6/(12 + 6) = 72/18 = 4Ω