Question

#Derive 1/R=1/R1+1/R2+1/R3. COMMON THE EASY ONE WHO WILL SOLVE IT? #PARALLEL CONNECTION#

Answer 1

Answer:

Consider three resistors having resistance R1, R2 and R3 are connected in parallel as shown in dig. Let r be the potential difference applied across the combination which is same for each resistor but current flowing through each resistor is different and total current is given by:

I = I1 + I2 + I3 (i)

by ohm's law : current is given by I = V/ Rp (ii)

(where Rp = equivalent resistance of parallel combination)

also, I1 = current flowing through resistance

R1 = V/ R1 (iii)

I2 = current flowing through resistance

R2 = V/ R2 (iv)

I3 = current flowing through resistance

R3 = V/ R3 (v)

putting the values from (ii), (iii), (iv) and (v) in equation (i)

V/Rp = V/ R1 + V/ R2 + V/ R3

V/Rp = V ( 1/R1 + 1/R2 + 1/R3)

OR

1/Rp = 1/R1 + 1/R2 + 1/R3