How can three resistors of resistances 2 Ω,3 Ω and 6 Ω be connected to give a total resistance of (i) 4

(i) To get a total resistance of 4 Ω, you can connect the 2 Ω and 3 Ω resistors in parallel, and then connect this combination in series with the 6 Ω resistor.

Here's the step-by-step process:

Step 1: Connect the 2 Ω and 3 Ω resistors in parallel. The total resistance (R1) of two resistors in parallel can be calculated using the formula 1/R1 = 1/R2 + 1/R3. Substituting the given values, we get 1/R1 = 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Therefore, R1 = 6/5 = 1.2 Ω.

Step 2: Connect this combination in series with the 6 Ω resistor. The total resistance of resistors in series is simply the sum of the individual resistances. Therefore, the total resistance (Rt) is Rt = R1 + R4 = 1.2 Ω + 6 Ω = 7.2 Ω.

However, this does not give a total resistance of 4 Ω as required. Therefore, it is not possible to connect the three resistors to get a total resistance of 4 Ω.

(i) To get a total resistance of 4 Ω, you can connect the 2 Ω and 3 Ω resistors in parallel, and then connect this combination in series with the 6 Ω resistor.

Here's how:

Step 1: Connect the 2 Ω and 3 Ω resistors in parallel. The total resistance (R1) of two resistors in parallel can be calculated using the formula 1/R1 = 1/R2 + 1/R3. Substituting the given values, we get 1/R1 = 1/2 + 1/3 = 3/6 + 2/6 = 5/6. Therefore, R1 = 6/5 = 1.2 Ω.

Step 2: Connect this combination in series with the 6 Ω resistor. The total resistance of resistors in series is simply the sum of the individual resistances. Therefore, the total resistance (Rt) is Rt = R1 + R4 = 1.2 Ω + 6 Ω = 7.2 Ω.

However, this does not give a total resistance of 4 Ω as required. Therefore, it is not possible to connect the three resistors to get a total resistance of 4 Ω.