Question

Two wires A and B are made of the same material and have the same diameter. Wire A is twice as long as wire B. If each wire has the same potential difference across its ends, which one of the following statements is true concerning the current in wire A?

a. The current is half as much as that in B.
b. The current is one-fourth that in B.
c. The current is equal to the current in B.

Answer 1

a. truth

b. false

c. false

Step-by-step explanation:

We have to take into account that the resistance is given by:

`R=\rho(L)/(S)` (1)

where p is the resistivity of the material, L is the length, and S is the transverse area of the material.

In this case we have that the relation between the lengths of the wires are

`L_A=2L_B`

Hence, by taking into account tha both wire has the same S:

`R_B=\rho(L_B)/(S)\\R_A=\rho(L_A)/(S)=\rho(2L_B)/(S)=2R_B\\` (2)

Furthermore, due to both wires have the same potential we obtain:

`I_B=(V)/(R_B)\\I_A=(V)/(R_A)=(V)/(2R_B)=(1)/(2)I_B\\` (3)

a.

truth, because of the result in (3)

b.

false

c.

false

hope this helps!

Answer 2

a. The current is half as much as that in B

Step-by-step explanation:

If the two wire of the same material, then they have the same resistivity

Given that the diameter of the two wire are equal, this shows that the cross-sectional area are equal.

Length of wire A is twice the length of wire B

Let Wire B be x meter long

Then, Length of wire A is 2x meter long

The same potential difference is passed between the two wires

Then, Va = Vb

From the formula of resistance,

R = pL/A

Where R is resistance

p is resistivity

L is length of wire

A is the cross-sectional area

From here,

Resistance of wire A

Ra = p•2x/A = 2px/A

Resistance of wire B

Rb = pxA

It is notice that Ra = 2Rb

The resistance of wire A is twice the resistance of wire B

So, if equal voltage are passed,

Then, using ohms law

V= IR

For wire A

Ia = V/Ra = ½ V/Rb

For wire B

Ib = V/Rb

Then, Ia = ½Ib

The current in wire A is half as much the current in wire B

The first option is correct