Question

32. Show that how would you connect three resistors each of resistance 612, so that the combination has a
resistance of i) 9 (ii) 4​

Answer 1

(i)

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

Since, R

eq

=R

1

+R

2

9=6+R

2

R

2

=3 Ω

⟹R

2

<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,

R

eq

1

=

R

1

1

+

R

2

1

9

1

=

6

1

+

R

2

1

R

2

=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.