Question

You have two metallic wires of resistances 60 and 30. How will you connect these wires to get the effective resistance of 20 ?​

Answer 1

$\bigstar$ Given

You have two metallic wires of resistances 60 and 30

$\bigstar$ To Find

How to connect these wires to get the effective resistance of 20

$\bigstar$ Solution

We know that

$\red{\sf \longrightarrow \dfrac{1}{R_{p}}=\dfrac{1}{R_{1}}+\dfrac{1}{R_{2}}}$

On further simplification

We get

$\pink{\sf \longrightarrow R_{p}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}} \ \Omega}$

Here

• $\bold{\sf R_{p}}$ = Resistance in parallel
• R₁ = Given resistance (1)
• R₂ = Given resistance (2)

According to the question

We are asked to find how to connect these wires to get the effective resistance of 20

Given that

You have two metallic wires of resistances 60 and 30

Hence

• R₁ = 60 Ω
• R₂ = 30 Ω

Substituting the values

We get

$\blue{\sf \longrightarrow R_{p}=\dfrac{60 \times 30}{60+30}}$

On further simplification

We get

$\green{\sf \longrightarrow R_{p}=\dfrac{1800}{90} \ \Omega}$

Hence

$\orange{\sf \longrightarrow R_{p}=20 \ \Omega}$

Therefore

Effective resistance of 20 Ω can be gained by connecting them in parallel

Answer 2

Given:-

• You have two metallic wires of resistances 60 and 30.

To Find:-

• How to connect these wires to get the effective resistance of 20.

Solution:-

Formula : -

$\pink{\sf ➜ R_{p}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}} \ \Omega}$

where,

$\sf R_{p}= Resistance\: in\: parallel$

R₁ = Given resistance (1)

R₂ = Given resistance (2)

Given that ,

R₁ = 60 Ω

R₂ = 30 Ω

Substituting the values,

$\sf \implies R_{p}=\dfrac{60 \times 30}{60+30}$

$\sf \implies R_{p}=\dfrac{1800}{90} \ \Omega$

$\boxed{\pink{\sf \implies R_{p}=20 \ \Omega}}$

Therefore,

Effective resistance of 20 Ω can be gained by connecting them in parallel

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