Question

A battery connected to two wires in parallel. Both wires are made of the same material and are of the same length, but the diameter of wire A is twice the diameter of wire B.
True or False for the following:
1) The resistance of wire B is four times as large as the resistance of wire A.
2) The power dissipated in wire A is 16 times the power dissipated in wire B.
3) The voltage drop across wire B is larger than the voltage drop across wire A.
4) The resistance of wire B is twice as large as the resistance of wire A.
5) The current through the battery is five times larger than the current through wire B.

Answer 1

Answer:

true  1

2 is false   2. 3 . 4. 5  

Explanation:

For this exercise, let's calculate the different parameters and analyze the corresponding statements.

the resistance of each wire

         R = ρ $\frac{L}{A}$

wire B.

has a diameter of d₀

therefore its radius is r₀ = d₀ / 2

the area is A = pi r₀²

                     A = π d₀²/ 4

we subtitle

          Ro = ρ $\frac{L \ 4}{\pi d_o^2}$

          R_b = R₀

wire A

the diameter is d = 2d₀

therefore the radius is r = d/2

                        r = d₀

resistance is

              R_a = ρ $\frac{L}{\pi d_o}$

   

              R_a = 4 R₀

when examining the answers

1 is true

4 is false

Now let's calculate the power

         P = V I

         V = I R

         P = V² / R

as they indicate that the cables are connected in parallel, the voltage in them is the same, therefore the potency depends on the resistance

         

wire B  

         P = V² / R_b

          P_b = V² / R₀

wire A

          P_a = v² / R_a

          P_a = V² / 4R₀

          P_a = ¼ P_b

2 is false

in a parallel circuit the waves are the same therefore

3 False

ohm's law is

         V = I r

         I = V / R

   

wire B

       I_b = V / R_b

       I_b = V / Ro

wire

       I_a = V / R_a

       I_a = V / 4 Ro

       I_a = ¼ I_a

5 is false