Question

The class is provided with 2 ohm, 3 ohm and 6 ohm. What is the maximum resistance that can be made using all three?​

Answer 1

Solution

Given :-

There are three resistors of resistances 2 Ohm, 3 Ohm, and 6 Ohm respectively.

Let R₁ = 2 Ω

R₂ = 3 Ω

R₃ = 6 Ω

(a) Total resistance 4 ohm

To obtain a total resistance of 4 Ω from three resistors of given resistances, Firstly, connect the two resistors of 3Ω and 6Ω in parallel to get a total resistance of 2Ω which is less than the lowest individual resistance.

When R2 and R3 are connected in parallel with R₁ in series we get

⇒ 1/R = 1/R₂ + 1/R₃

⇒ 1/R = 1/3 + 1/6

⇒ 1/R = 1/2

⇒ R = 2 Ω

⇒ Resistance in series = R + R₁=2 + 2 = 4 Ω

Hence, the total resistance of the circuit is 4 Ω.

(b) To obtain a total resistance of 1Ω from three resistors of 2Ω, 3Ω and 6Q, all the three resistors should be connected in parallel.

When R₁, R₂, R₃ are connected in parallel we get

⇒ 1/R = 1/R₁ + 1/R₂ + 1/R₃

⇒ 1/R = 1/2 + 1/3 + 1/6

⇒ 1/R = 1 Ω.

Hence, the total resistance of the circuit is 1 Ω.