Question

25
5
Questions Based on High Order Thinking Skills (HOTS)
43. Show with the help of diagrams, how you would connect three resistors each of resistance 6ohm, so that the
combination has resistance of (i) 9ohm (ii) 4 ohm
​

Answer 1

Answer:

4 ohm

Explanation:

We are given 3 resistors each of resistance 6 Ω. Equivalent resistance of resistors in series is more than the individual resistance of each resistor while equivalent resistance of resistance in parallel is less than the individual resistance of each resistor. 

(i)

To get an equivalent resistance of 9 Ω, atleast one six ohm resistor should be connected in series with the other resistors. 

Since, Req=R1+R2

9=6+R2

R2=3 Ω

⟹R2<6 Ω

Connecting the remaining two resistors in parallel will yield an equivalent resistance of 3 Ω.

Hence, the first figure shows the configuration of resistors to get equivalent resistor of 9 Ω. 

(ii)

To get an equivalent resistance of 9 Ω, no six ohm resistor should be connected in series with the other resistors. 

Let one of the branches have only one 6 Ω resistor.

Since, Req1=R11+R21

91=61+R21

R2=12 Ω

Connecting the remaining two resistors in series will yield an equivalent resistance of 12 Ω.

Hence, the second figure shows the configuration of resistors to get equivalent resistor of 4 Ω