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3 years ago

A conducting wire is quadrupled in length and tripled in diameter.

Physics

2 answers:

aivan3 [116]3 years ago

7 0

Answer:

Its resistance decreases

Explanation:

The resistance of a wire is directly proportional to the length of the wire and inversely proportional to the cross sectional area of the wire.

Mathematically,

R1 =¶L1/A1... (1)

R1= ¶L1/{Πd²/4}

R1= 4¶L1/Πd²

where;

¶ is the constant of proportionality which is the resistivity of the material

L is the length of the wire

A is the cross sectional area

A1 = Πd²/4

If the length is quadrupled and its diameter tripled

The new length L2 will be 4L1

New area A2 = Π(3d)²/4 = 9Πd²/4

The resistance will become

R2 = ¶(4L1)/{9Πd²/4}

R2 = 4¶L1×4/9Πd²

R2 = 16¶L1/9Πd²... (2)

R2/R1 = 16¶L1/9Πd²÷4¶L1/Πd²

R2/R1 = 16¶L1/9Πd²×Πd²/4¶L1

R2/R1 = 16/9×1/4

R2/R1 = 16/36

R2/R1 = 4/9

R2 = 4/9R1

This shows that the resistance of the wire decreases

Karo-lina-s [1.5K]3 years ago

4 0

Explanation:

Below is an attachment containing the solution.

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3 years ago

Read 2 more answers

When a gas is heated, it absorbs 196 joules of heat from the surroundings. At the same time, the gas expands, doing pressure-vol

timurjin [86]

Answer:

(a) q positive; w negative.

(b) ΔE = -126 J

Explanation:

(a) Determine whether the amounts of heat (q) and work (w) exchanged should have positive or negative signs. heat (q) positive negative work (w) positive negative

By convention, when the system absorbs heat from the surroundings, its sign is positive, that is, q = 196 J.

By convention, when the system exerts work on the surroundings, its sign is negative, that is, w = -322 J.

(b) Calculate the change in internal energy (ΔE) of the gas. J

The change in internal energy (ΔE) can be calculated using the following expression.

ΔE = q + w

ΔE = 196 J + (-322 J) = -126 J

(c) Determine whether one or more of the following is a state function:

internal energy (E) of a system,

change in internal energy (ΔE) of a system,

heat (q) absorbed or released by a system,

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2 years ago

A long solenoid with 8.22 turns/cm and a radius of 7.00 cm carries a current of 19.4 mA. A current of 3.59 A exists in a straigh

daser333 [38]

Answer:

a. 3.039cm

b.magnetic field is $B=2.958\times10^{-5}T$

Explanation:

Direction of the solenoid magnetic field is along the axis of the solenoid. and magnetic field due to the wire perpendicular to that due to the solenoid.. Magnetic field at r is given by:

$\overrightarrow B = \overrightarrow B_s+ \overrightarrow B_w,\ \ \ \ \ \overrightarrow B_s\perp \overrightarrow B_w$

Angle of net magnetic field from axial direction is given by:

$tan\ \theta=\frac{B_w}{B_s}$ ,

Field due to solenoid:

$B_s=\mu_onI_s, \ \ \ \ n=(8.22 t/cm)(100cm/m)=822turn/m$

Field due to wire:

$B_w=\frac{\mu_oI_w}{2\pi r}$

Therefore, r:

$tan\ \theta=\frac{B_w}{B_s}\\\\=\frac{\mu_oI_w}{2\pi r(\mu_o nI_s)}\\\\r=\frac{I_w}{2\pi nI_stan \ \theta}\\\\r=\frac{3.59A}{2\pi\times822\times19.4\times10^{-3}A \ tan 49.7\textdegree}\\\\r=3.039cm$

Hence, the radial distance is 3.039cm

b.The magnetic field strength is given by:

$B=\sqrt{B_w^2+B_s^2}\\\\tan 49.7\textdegree=\frac{B_w}{B_s}\\\\1.179=\frac{B_w}{B_s}\\\\B_w=1.179B_s\\\\B=\sqrt{(4\pi\times10^{-7}T.m/A\times 822\times19.4\times10^{3}A)+1.179(4\pi\times10^{-7}T.m/A\times 822\times19.4\times10^{-3}A)}\\\\B=2.958\times10^{-5}T$

Hence, the magnetic field is $B=2.958\times10^{-5}T$

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3 years ago