Question

two resistors of 5 ohm and 10 ohm are connected in series and 15 ohms and 20 ohm are series both are parallel find the equivalent resistance​

Answer 1

Answer :

The required equivalent resistance is 10.5 Ω

Explanation :

Given :

• two resistors of 5 Ω and 10 Ω are connected in series
• another two resistors of 15 Ω and 20 Ω are in series

• both these connections are connected in parallel

To find :

the equivalent resistance

Solution :

In series combination, the equivalent resistance is given by

  $\underline{\boxed{\sf R_s=R_1+R_2}}$

For the first series combination,

Put R₁ = 5 Ω and R₂ = 10 Ω

 Rₛ = 5 Ω + 10 Ω

 Rₛ = 15 Ω

For the second series combination,

Put R₁ = 15 Ω and R₂ = 20 Ω

 Rₛ' = 15 Ω + 20 Ω

 Rₛ' = 35 Ω

Now, Rₛ and Rₛ' are connected in parallel.

In parallel connection, the equivalent resistance is given by

  $\underline{\boxed{\sf R_p=\dfrac{R_1R_2}{R_1+R_2}}}$

Put R₁ = Rₛ and R₂ = Rₛ'

Substitute the values,

  $\sf R_p=\dfrac{15 \times 35}{15+35} \\\\ \sf R_p=\dfrac{525}{50} \\\\ \sf R_p=\dfrac{105}{10} \\\\ \sf R_p=10.5 \ \Omega$

The equivalent resistance of the whole combination of resistors = 10.5 Ω