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

true 1

2 is false 2. 3 . 4. 5

Step-by-step explanation:

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

the resistance of each wire

R = ρ
`(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
`(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
`(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