1)a piece of copper wire was cut into "n" equal parts. these parts are connected in parallel. how will the

Question

resistance of the parallel combination compare with the resistance of the wire?.........2)strings of Christmas lights were made of miniature lamps connected in series. if one lamp is removed, what would happen???

Answer 1

1:

I will answer this by first looking at a similar problem. Take a 1000 Ohm resistor. Put it in parallel with another 1000 Ohm resistor. You now have 1000//1000=500 Ohms OR 1000/2.

Now take another 1000 Ohm Resistor and parallel with the other two. You now have 1000//1000//1000=333.3 Ohms OR 1000/3. Note that the divisor is always the same as the number of resistors.

To answer your question. Rtotal=(the original value/n)/n OR Roriginal/n^2

2:One lamp removed = no lights.

Answer 2

a) 1/Reff = 1/R1 + 1/R2 but since R1 and R2 are equal because they have the same material, 1/Reff = 2/R1 (Reff - effective resistance | R1, R2 - resistance of each resistor / object with resistance)

b) if one lamp from the Christmas lights is removed, all of the light bulbs remaining will not work. series circuit is the least option of circuit type when you have multiple sockets / plugs because it will affect the others.

Answer 3

1)a piece of copper wire was cut into "n" equal parts. these parts are connected in parallel. how will the

resistance of the parallel combination compare with the resistance of the wire?.........

Call the resistance of the wire Rw and the final parallel resistance Rp.

The resistance of each piece of wire is Rw / n.

The formula for parallel resistance is:

R = 1 / [(1 / R1) + (1 / R2) + (1 / R3)......]

In this case:

Rp = 1 / [(1 / (Rw / n)) + (1 / (Rw / n)) + (1 / (Rw / n))....]

Simplifying:

Add the 1 / (Rw / n) terms:

Rp = 1 / ( n / (Rw / n))

Take reciprical of Rw / n and multiply:

Rp = 1 / (n * (n / Rw))

or

Rp = 1 / (n^2 / Rw)

Take reciprocal of n^2 / Rw and multiply:

Rp = Rw / n^2

At n = 2, Rp = Rw / 4. At n = 3, Rp = Rw / 9, etc,

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In a series-connected set of lights, if one lamp is removed, they will all go out because the circuit is broken.

Answer 4

If R is the original resistance of the wire.

n parts each have a resistance of R/n

putting them in parallel makes the resistance R/n²

2) All the lights would go out is the simplistic answer.