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.

Q.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.

 

Answer:-

(i) Two resistors in parallel

chapter12zf.jpg

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

chapter12zh

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
chapter12zi
Here Rs=6+6=12 Ω let third resistance R3=6 Ω
Two 6 Ω resistors are in series. Their equivalent resistance will be the sum
chapter12zj
∴ the total resistance is 4 Ω.