Answer:
a. The current is half as much as that in B
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
Answer:
a. truth
b. false
c. false
Explanation:
We have to take into account that the resistance is given by:
[tex]R=\rho\frac{L}{S}[/tex] (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
[tex]L_A=2L_B[/tex]
Hence, by taking into account tha both wire has the same S:
[tex]R_B=\rho\frac{L_B}{S}\\R_A=\rho\frac{L_A}{S}=\rho\frac{2L_B}{S}=2R_B\\[/tex] (2)
Furthermore, due to both wires have the same potential we obtain:
[tex]I_B=\frac{V}{R_B}\\I_A=\frac{V}{R_A}=\frac{V}{2R_B}=\frac{1}{2}I_B\\[/tex] (3)
a.
truth, because of the result in (3)
b.
false
c.
false
hope this helps!
