Derive for parallel connection equivalent resistance(r) = \frac{R1*R2}{R1+R2}

Answers (1)
S safeer

In a parallel circuit, the voltage across the resistors remains the same but the current get distributed. That is 

\\I=I_1+I_2

If R is the total resistance of the circuit then 

\\I=\frac{V}{R}

Therefore

\\\frac{V}{R}=\frac{V}{R_1}+\frac{V}{R_2}\\or\ \frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}\\\\orR=\frac{R_1R_2}{R_1+R_2}

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