Question

resistor of 3.6 ohm is connected in series with another resistance of 4.6 ohm.what resistance (R) must be connected across 3.6ohm so that the total resistance of circuit is 6ohm

Answer 1

See the above solution ☺

Answer 2

Resistor of 3.6 ohm is connected in series with another resistance of 4.6 ohm.

What resistance must be connected across 3.6 ohm so that the total resistance of circuit is 6 ohm.

3.6 ohm and 4.6 ohm are connected in series so if we find equivalent resistance of it, we get

R = 3.6 + 4.6 = 8.2 ohm ,

• It is greater than the total resistance of circuit (i.e., 6 ohm ) after connecting another resistor across 3.6 ohm.

• It is possible only possible if we join unknown resistor across 3.6 in parallel combination.

∵ equivalent resistance of two resistors joined in parallel is given by R = R₁R₂/(R₁ + R₂)

∴ equivalent of 3.6 ohm and unknown resistor x is

R = (3.6x)/(3.6 + x).

now R joined in series with 4.6 ohm.

so final equivalent resistance , Req = (3.6x)/(3.6 + x) + 4.6 = 6

⇒ (3.6x)/(3.6 + x) = 1.4

⇒ 3.6x = 3.6 × 1.4 + 1.4x

⇒ 2.2x = 5.04

⇒ x ≈ 2.3 ohm

Therefore the another resistance is 2.3 ohm.