## 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.

Note:-If all 3 resistance were different, we would have 8 cases check

Last updated at Aug. 6, 2019 by Teachoo

Note:-If all 3 resistance were different, we would have 8 cases check

Transcript

NCERT Question 11 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. This can be done in 4 ways All 3 in series All 3 in parallel 2 in parallel, 1 in series 2 in series, 1 in parallel In series combination, equivalent resistance is given by Rs = R1 + R2 + R3 In parallel combination, equivalent resistance is given by 1/𝑅_𝑃 = 1/𝑅_1 + 1/𝑅_2 + 1/𝑅_3 Case I All are connected in series R = 6 + 6 + 6 = 18 Ω Case II All are connected in parallel 1/𝑅 = 1/6 + 1/6 + 1/6 1/𝑅 = 3/6 1/𝑅 = 1/2 R = 2 Ω Case III 2 resistors connected in series and 1 parallel to them First we’ll find equivalent of resistors in series RS = 6 + 6 = 12 Ω Now the circuit becomes Thus, equivalent resistance becomes 1/𝑅 = 1/12 + 1/6 1/𝑅 = (1 + 2)/12 1/𝑅 = 3/12. 1/𝑅 = 1/12 R = 4 Ω Case IV 2 resistors connected in parallel and 1 connected in series with them First we’ll find equivalent of resistors in parallel 1/𝑅_𝑝 = 1/6 + 1/6 1/𝑅_𝑝 = 2/6 1/𝑅_𝑝 = 1/3 Rp = 3 Ω Now the circuit becomes Thus, equivalent resistance becomes R = 3 + 6 = 9 Ω Therefore, To give total resistance of 9 Ω Case IV Connect 2 resistors in parallel and 1 resistors in series with them (b) To give total resistance of 4 Ω Case III Connect 2 resistors in series and 1 resistors parallel to them

NCERT Questions

NCERT Question 1

NCERT Question 2

NCERT Question 3

NCERT Question 4

NCERT Question 5

NCERT Question 6

NCERT Question 7

NCERT Question 8

NCERT Question 9

NCERT Question 10

NCERT Question 11 You are here

NCERT Question 12

NCERT Question 13

NCERT Question 14

NCERT Question 15

NCERT Question 16

NCERT Question 17

NCERT Question 18 (a)

NCERT Question 18 (b)

NCERT Question 18 (c)

NCERT Question 18 (d)

NCERT Question 18 (e)

Class 10

Chapter 12 Class 10 - Electricity

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.