Question

if the equivalent resistance is 4.5 ohms then find the value of R in the circuit?​

Answer 1

Answer:

Req = 3/3 +R

so R= Req - 1 = 4.5-1 = 3.5 ohm

Answer 2

Solution:

According to the given circuit diagram, we are given that the total resistance of the combination of these resistors is 4.5 ohms.

Calculating the net resistance we get:

→ Net Resistance = Net resistance of Parallel Combination + R

Calculating Net resistance of Parallel combination we get:

$\text{Net Resistance of Parallel Combination:}\\\\\boxed{ \dfrac{ 1}{R_{p}} = \dfrac{1}{R_1} + \dfrac{1}{R_2} + \dfrac{1}{R_3} .... + \dfrac{1}{R_n}}$

According to the question,

• R₁ = 3 ohms
• R₂ = 3 ohms

Applying the formula we get:

$\implies \dfrac{1}{R_p} = \dfrac{1}{3} + \dfrac{1}{3} \\\\\\\implies \dfrac{1}{R_p} = \dfrac{2}{3}\\\\\\\implies R_p = \dfrac{3}{2} = 1.5 \:\Omega$

Hence Total Resistance is given as:

→ 4.5 Ω = 1.5 Ω + R

→ R = 4.5 Ω - 1.5 Ω

→ R = 3 Ω

Hence the value of R in the circuit is 3 Ω