Question

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

Answer 1

See let there be n resistors of resistance r1,r2,r3 ...... rn 

so in parallel connection the potential difference remains same 

but the current spreads in different resisters in i1,i2,i3 ...... in

so let the total potential difference be V current be I and equivalent resistance be R

so using junction rule I = i1 + i2 + i3 + . . . + in

so we know I = $\frac{V}{R}$  from Ohm's Law

so $\frac{V}{R}= \frac{V}{r1}+\frac{V}{r2}+\frac{V}{r3}+....+\frac{V}{rn}$

cancelling V from both sides we get 


$\frac{1}{R}= \frac{1}{r1}+\frac{1}{r2}+\frac{1}{r3}+....+\frac{1}{rn}$   


PROVED

Answer 2

Please see the attachment ....I hav done the derivation for two resistors