Question

You are given a number of 10 Ω resistors, each capable of dissipating only 3.0 W without being destroyed. What is the minimum number of such resistors that you need to combine in series or in parallel to make a 10 Ω resistance that is capable of dissipating at least 8.6 W?

My answer is 1 which is wrong idk why pls help. Tried searching it.. I got wrong

Answer 1

Power = I^2R

so what current is required, through 10 ohms to give 8.6W?

Answer 2

Okay then?

Answer 3

The question is kinda tricky for me. So maybe I got wrong in the reading comprehension what I did is 8.6=(x/10)^(-1) and I got wrong

Answer 4

I'll rethink this ...

The resultant resistance is required to be 10 ohms

you start with 10 ohm resistors

if you put them in parallel you reduce the resistance
if you put them in series you increase the resisistance

so - can you deduce the layout of the combination that will remain 10 ohms?

Answer 5

Hmm I getting lost sir.. can you please guide me more.

Answer 6

you are require to make a combination of reistors

the result of the combination must be 10 ohms
but each individual resitor is 10 ohm

so for instance
if you put 2 in parallel you reduce the resistance to 5ohms
if you put 2in series you increase the resisistance to 20 ohms

so how would you arrange the resistors so that the resultant resistance is 10 ohms?

Answer 7

So you only need 1?

Answer 8

Uh wait
hmm

Answer 9

2 parallel resistors and 0 series resistors?

Answer 10

no - because 1 can only withastand 3W power
you need to make a combination that can dissipate at least 8.6W

BUT the combination must also have a resistance of 10 ohms

Answer 11

if you put 2 in parallel you reduce the resistance to 5ohms

Answer 12

I need to get a 9?

Answer 13

it dissipates 8.6 and less than 10

Answer 14

or wait I need 3 resistors?

Answer 15

do you understand the rlationship between current ,resistance and power?

also the parallel and series resistance equations?

Answer 16

I know the formula... which is kinda a problem maybe? I'm so used on calculating that I forgeting the true concept of the topic

Answer 17

so - your guess of 3 cannot be true - how would you make 10 ohms resultant from 3 10 ohm resistors?

Answer 18

oh my I'm so getting lost..

Answer 19

so
using W = I^2 R

you need to work out th current require dto get 8.6 W through 10 ohms
AND
The maximaum current that can pass through 1 of the original resistors

Answer 20

Okay so by that formula I can get it? HMm wait

Answer 21

No - that is the starting point

you need to know the current before you can work out the answer

Answer 22

W = 8.6 right

Answer 23

then R = 10?

Answer 24

yes = so work out I from
W = I^2 R

Answer 25

So I got I = 0.9274 what's next?

Answer 26

OK - so that is the minimum current that must pass through the combination of resisstors, in order to get at least 8.6W

So NOW
What is the maximum current that can pass through 1 of the original 10 ohm resistors if the power is 3W

Answer 27

so work out I from
W = I^2 R

Answer 28

Okay maximum eh.. Hmmm thinking

Answer 29

maximum current is when power is maximum -

so max current is when w=3, r=10

Answer 30

will I change 8.6W into 3W?

Answer 31

3=(I)^2(10) ??

Answer 32

yes

Answer 33

I goy 0.55

Answer 34

ok - correct

SO

you can see now why you cannot use 1 resistor - the current is too high - it will burn out

so


if the 2 resistances are equal then how much current flows through each resisttance?