You have two metallic wires of resistances 60 and 31. How will you connect these wires to get the effective
resistance equal to 212?
Answers
Explanation:
\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}}}⟶Rp1=R11+R21
On further simplification
We get
\pink{\sf \longrightarrow R_{p}=\dfrac{R_{1}R_{2}}{R_{1}+R_{2}} \ \text{\O}mega}⟶Rp=R1+R2R1R2 Ømega
Here
\bold{\sf R_{p}}Rp = 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}}⟶Rp=60+3060×30
On further simplification
We get
\green{\sf \longrightarrow R_{p}=\dfrac{1800}{90} \ \text{\O}mega}⟶Rp=901800 Ømega
Hence
\orange{\sf \longrightarrow R_{p}=20 \ \text{\O}mega}⟶Rp=20 Ømega
Therefore
Effective resistance of 20 Ω can be gained by connecting them in parallel