How many 330 ohm resistors must be connected in parallel to obtain a Req of 5 ohms

To find the number of resistors ( n ) needed in parallel to achieve an equivalent resistance ( R_{eq} ) of 5 ohms, we use the formula for resistors in parallel:

\frac{1}{R_{eq}} = \sum \frac{1}{R_i}

Since all resistors ( R_i ) have the same resistance (330 ohms), the formula becomes:

\frac{1}{R_{eq}} = n \left( \frac{1}{R} \right)

Rearranging to solve for n :

n = \frac{R}{R_{eq}}

Given R = 330 ohms and R_{eq} = 5 ohms:

n = \frac{330}{5} = 66

Thus, the number of resistors needed is:

n=66