How many 16 ΩΩ resistors must be connected in series to give an equivalent resistance to five 800 ΩΩ resistors connected in parallel?
Question
How many 16 Ω resistors must be connected in series to give an equivalent resistance to five 800 Ω resistors connected in parallel?
Solution
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.
Similar Questions
What is the minimum resistance which can be made using five resistors each of 1/5 Ω?
How many resistors of 88 Ω are connected in parallel to carry 10 A current on a 220 V line ?
Four resistors of 4 ohm each are connected in parallel, four such combinations are then connected in series. Their total resistance is
Look at the diagram below. Are the resistors connected in series or in parallel?
How can three resistors of resistances 2 Ω,3 Ω and 6 Ω be connected to give a total resistance of (i) 4
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.