A common resistance of carbon resistors is 33 Ω . How many 33 Ω resistor, connected in parallel, are needed to give a total resistance of 5.5 Ω ?

Question

A common resistance of carbon resistors is 33 Ω . How many 33 Ω  resistor, connected in parallel, are needed to give a total resistance of 5.5 Ω ?

mathmate · Answer

Resistors connectors connected in parallel are given by the formula:
1/R=(1/R1+1/R2+1/R3....+1/Rn)
if each of n resistors are 33$\Omega$, then the equation becomes
1/R=(1/33+1/33+....+1/33)  .............(n times)
=n/33.......................(1)
Since the final resistance needs to be 5.5$\Omega$, substitute R=5.5 in equation (1) and solve for n.