Question

.Five resistors of 2 ohm are connected as parallel, find the effective resistance?

Answer 1

AnswEr :

As per the provided information in the given question, it has been stated that the five resistors of 2Ω are connected in the parallel combination. We've been asked to calculate the effective resistance. Considering the provided information, we have :

• R₁ = 2Ω
• R₂ = 2Ω
• R₃ = 2Ω
• R₄ = 2Ω
• R₅ = 2Ω

Basically, in order to calculate the effective resistance of the given resistors connected in the parallel combination, we need to apply the formula to calculate the effective resistance of the circuit when the resistors are connected in the parallel combination. As we know that, when resistors are connected in the parallel combination, then effective resistance is given by,

$\longrightarrow \boxed{\tt { \dfrac{1}{R_P} = \dfrac{1}{R_1} +\dfrac{1}{R_2} + \dots \dfrac{1}{R_n}} }$

Here, we have 5 resistors so,

$\longrightarrow \tt { \dfrac{1}{R_P} = \dfrac{1}{R_1} +\dfrac{1}{R_2} + \dfrac{1}{R_3}+ \dfrac{1}{R_4} + \dfrac{1}{R_5} } \\ \\\longrightarrow \tt { \dfrac{1}{R_P} = \dfrac{1}{2} +\dfrac{1}{2} + \dfrac{1}{2}+ \dfrac{1}{2} + \dfrac{1}{2}} \\ \\ \longrightarrow \tt { \dfrac{1}{R_P} = \dfrac{1 + 1 + 1 + 1 + 1}{2} } \\ \\ \longrightarrow \tt { \dfrac{1}{R_P} = \dfrac{5}{2}} \\ \\ \longrightarrow \tt { R_P = \dfrac{2}{5}} \\ \\ \longrightarrow \underline{\boxed{\tt { R_P = 0.4 \; \Omega} }} \;\red{\bigstar}$

Therefore, the effective resistance is 0.4 Ω.

⠀⠀⠀⠀⠀_____________

Points to remember :

When resistors are connected in the parallel combination, then effective resistance is given by,

$\longrightarrow \boxed{\tt { \dfrac{1}{R_P} = \dfrac{1}{R_1} +\dfrac{1}{R_2} + \dots \dfrac{1}{R_n}} }$

When resistors are connected in the series combination, then effective resistance is given by,

$\longrightarrow \boxed{\tt { R_P = R_1 + R_2 + \dots R_n} }$