Question

show that how will you connect three resistors of 12 ohm each show that the combination has a resistance of 8 ohm​

Answer 1

Given:-

• Resistance of Resistor ,R1 = 12 Ω

• Resistance of Resistor ,R2 = 12 Ω

• Resistance of Resistor ,R3 = 12 Ω

To Find:-

• How will we connect the Resistors to get the equivalent resistance of 8 ohm.

Solution:-

IF we connect the two Resistors in series and 1 Resistor in parallel then we get the total equivalent resistance is 8 ohms. Now, Let's Prove it .

As we know that the Equivalent Resistance in Series is the Sum of resistance of each resistors .

• Req (In Series) = R1 + R2

Substitute the value we get

→ Req = 12 + 12

→ Req = 24 Ω

Equivalent Resistance in Series is 24 ohms.

Now connect this equivalent Resistance in remaining Resistor in Parallel.

• 1/Req' (In Parallel) = 1/Req (in Series) + 1/R3

Substitute the value we get

→ 1/Req' = 1/24 + 1/12

→ 1/Req' = 1+2/24

→ 1/Req' = 3/24

→ 1/Req' = 1/8

→ Req' = 8

Here,

Equivalent resistance of the Resistors are 8 ohms .

Therefore, Two Resistor must be connected in series and their equivalents resistance should be connected in parallel with remaining resistor .Then we get the Equivalent resistance 8 ohms.

Answer 2

In Series R1+ R2

=> 12 + 12

=> 24 ohm

Now

In Parallel

=>1/R = 1/24 +1/2

=> 1/R = 3/24

=> R = 24/3

=> R = 8 ohms

Hope this helps You