Scioly.org

I'm finalizing my binder for our state competition in PA, and I was wondering if anyone would like to share some of the harder questions they've been asked

Toms_42 wrote:I'm finalizing my binder for our state competition in PA, and I was wondering if anyone would like to share some of the harder questions they've been asked

We had a very interesting problem. In the problem, there is an arrangement of resistors, but you don't know how they're arranged. Then they take out each resistor and tell you the value of the currents passing through each of the other resistors. Using this info, you find the value/arrangement of all the resistors. You use your basic series/parallel concepts to find the configuration and then you can find the values. In the end, it was not that hard because all the resistors had the same value

Our NJ tiebreaker question was that there was a speaker and resistor set up in series. The value of the resistor was not known and the question was that if 4 exact same resistors were wired in parallel instead of that single resistor, would the speaker be louder or lower or no change at all (ie would the current be higher?)

UQOnyx wrote:Our NJ tiebreaker question was that there was a speaker and resistor set up in series. The value of the resistor was not known and the question was that if 4 exact same resistors were wired in parallel instead of that single resistor, would the speaker be louder or lower or no change at all (ie would the current be higher?)

what did you answer?

The correct answer would be that the current would go up and the speaker would be louder because when a circuit is wired in parallel, the total resistance must be less than any of the resistors, and since V=IR, the current would go up

fantasyfan wrote:The correct answer would be that the current would go up and the speaker would be louder because when a circuit is wired in parallel, the total resistance must be less than any of the resistors, and since V=IR, the current would go up

yup.
I was asking because I wasnt sure if he meant the 4 resistors were in parallel with the speaker (in which case it would stay the same) or if they were replacing the old one.

also why is that a tiebreaker?

(the best tiereaker ive seen was on the kenston meteo test: How many roofs does a METAR station have? correct answer was 2, we said 4, the JV team said 18 )

Actually the speaker would get louder weather they were replacing the old resistors or in parallel with the speaker, because if the just replaced the old resistor the equivalent resistance would still be lower(1/4 the original).

iwonder wrote:Actually the speaker would get louder weather they were replacing the old resistors or in parallel with the speaker, because if the just replaced the old resistor the equivalent resistance would still be lower(1/4 the original).

I meant they kept the old resistor AND added the new ones in parallel with the speaker, sorry for the confusion

if that is true then the speaker would get quieter

fantasyfan wrote:if that is true then the speaker would get quieter

Actually, lets do the calculations.

For this example, lets drop the first resistor in series with the speaker to simplify things, as I am only explaining that current remains the same when another resistor is added in parallel.

Lets go with these values:

Battery: 10v
Speaker:10 ohms
Equivalent Resistor in parallel with speaker: 10 ohms

Let's find the total resistance of the circuit:

1/r=1/10+1/10
1/r=2/10
R=5ohms

Now for the current through the speaker: (voltage is 10 volts for the resistor and the speaker, and the resistance for the speaker remains at 10 ohms:
i=v/r
I=10/10
I=1 ampere

Now lets view the alternative, no resistor.

Total resistance is 10, As it is just that Of the speaker.

Current, once again:

i=v/r
I=10v/10 ohms
I=1 ampere (again)

Both currents are 1 ampere, so the speaker plays just as loud both times.

Even though some current is bypassed around the speaker in the first circuit, this is made up for by the all around lower resistance, 5 ohms instead of 10, so the total current of the first circuit doubles, but is halved again by the resistor bypassing the speaker.