Show how you would connect three resistors, each of resistance 6 Ω

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.

Solution:

(i) Two resistors in parallel

Two 6 Ω resistors are connected in parallel. Their equivalent resistance will be

 

The third 6 Ω resistor is in series with 3 Ω. Hence, the net resistance of the circuit is 6 Ω + 3 Ω = 9 Ω.

(ii) Two resistors in series

 

 

Here R_s=6+6=12 Ω let third resistance R₃=6 Ω

Two 6 Ω resistors are in series. Their equivalent resistance will be the sum

 

∴ the total resistance is 4 Ω  .