How many 16 ΩΩ resistors must be connected in series to give an equivalent resistance to five 800 ΩΩ resistors connected in parallel?

Step 1: Find the equivalent resistance of five 800 Ω resistors connected in parallel.

The formula for total resistance (Rt) of resistors in parallel is given by 1/Rt = 1/R1 + 1/R2 + ... + 1/Rn.

In this case, all resistors have the same resistance (R = 800 Ω), so the formula simplifies to 1/Rt = n/R, where n is the number of resistors.

So, 1/Rt = 5/800.

Solving for Rt gives Rt = 800/5 = 160 Ω.

Step 2: Find the number of 16 Ω resistors needed to give the same resistance.

When resistors are connected in series, the total resistance is simply the sum of the individual resistances.

So, if each resistor has a resistance of 16 Ω, the number of resistors needed is Rt/16 = 160/16 = 10.

Therefore, 10 resistors of 16 Ω each are needed to give the same resistance as five 800 Ω resistors connected in parallel.