Question

Two resistors connected in parallel have an equivalent resistance of 3.6 ohms. If one resistor is 6 ohms find the other.

Answer 1

Answer :-

Resistance of the other resistor is 9 Ω .

Explanation :-

We have :-

→ Equivalent resitance = 3.6 Ω

→ Resistance of 1st resistor = 6 Ω

_______________________________

When two resistances are connected in parallel, the equivalent resistance is given by :-

R = R₁R₂/R₁ + R₂

Where :-

→ R is the equivalent resistance.

→ R₁ is the resistance of the 1st resistor.

→ R₂ is the resistance of the other resistor.

Substituting values, we get :-

⇒ 3.6 = [6 × R₂]/[6 + R₂]

⇒ 3.6[6 + R₂] = 6R₂

⇒ 21.6 + 3.6R₂ = 6R₂

⇒ 21.6 = 6R₂ - 3.6R₂

⇒ 21.6 = 2.4R₂

⇒ R₂ = 21.6/2.4

⇒ R₂ = 9 Ω

Answer 2

Given :-

Two resistors connected in parallel have an equivalent resistance of 3.6 ohms. If one resistor is 6 ohms

To Find :-

Other resistor

Solution :-

We know that

$\sf R_{Equivalent} = \dfrac{R_1\times R_2}{R_1 + R_2}$

$\sf 3.6 = \dfrac{6 \times R_2}{6+R_2}$

$\sf \dfrac{3.6}{1} = \dfrac{6 \times R_2}{6+R_2}$

$\sf 3.6(6+R_2) = 6\times R_2$

$\sf 21.6 + 3.6R_2 = 6R_2$

$\sf 21.6 = 6R_2 - 3.6R_2$

$\sf 21.6 = 2.4R_2$

$\sf \dfrac{21.6}{2.40} = R_2$

$\sf 9=R_2$