Question

Three resistances of 4 ohm, 8 ohm and 16 ohm are to be connected to a circuit. Which of the following arrangements would yield minimum current?

All three in series
All three in parallel
4 ohm and 8 ohm in series and 16 phm in parallel to them
4 ohm and 16 ohm in parallel to 8 ohm in series

Answer 1

Answer:

ANSWER

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, 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.8

Explanation: