1.

For the parallel combination of three resistors ,establish the relation.1/Rp=1/R1+1/R2+1/R3 where the symbols have their usual meanings.

Answer»

Given :

⟶ Three IDENTICAL resistors of resistanced R_1, R_2 and R_3 are connected in parallel.

To Prove :

➨ 1/R_p = 1/R_1 + 1/R_2 + 1/R_3

Solution :

➠ Let, three resistors are connected in parallel with a battery of voltage V.

✭ Remember :

  • Current passing through each resistor remains same in series connection.
  • Voltage drop across each resistor remains in parallel connection.

➠ Let, Net current flowing through circuit be I.

◕ Current through R_1 = I_1

◕ Current through R_2 = I_2

◕ Current through R_3 = I_3

➠ As per ohm's LAW current passing through a CONDUCTOR is directly PROPORTIONAL to the applied pd.

Mathematically, V = IR

\longrightarrow\tt\:I=I_1+I_2+I_3\\ \\ \longrightarrow\tt\:\dfrac{V}{R_p}=\dfrac{V}{R_1}+\dfrac{V}{R_2}+\dfrac{V}{R_3}\\ \\ \longrightarrow\tt\:\dfrac{V}{R_p}=V\:{\huge (}\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}{\huge )}\\ \\ \longrightarrow\boxed{\bf{\dfrac{1}{R_p}=\dfrac{1}{R_1}+\dfrac{1}{R_2}+\dfrac{1}{R_3}}}


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