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attashe74
2 months ago
8

An MRI machine needs to detect signals that oscillate at very high frequencies. It does so with an LC circuit containing a 15mH

coil. To what value should the capacitance be set to detect a 450 MHz signal?
Physics
1 answer:
inna [3.1K]2 months ago
0 0

Answer:

The required capacitance is C = 3.2 9 *10^{-16} \ F.

Explanation:

The problem states that:

   The induction of the LC circuit is  L = 15 mH = 15 *10^{-3} \ H.

   The frequency is  w = 450 \ MHz = 450 *10^{6} \ Hz.

The natural frequency can be expressed mathematically as:

        w = \frac{1}{\sqrt{LC} }.

In this equation, C represents capacitance. Thus,

=>    C = \frac{1}{L * w^2}.

By substituting the known values, we obtain

           C = \frac{1}{15 *10^{-3} * [450 *10^{6}]^2}.

           C = 3.2 9 *10^{-16} \ F.

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a) 3.56 x 10^22 N. b) 3.56 x 10^22 N. The sun’s mass is M = 2 x 10^30 kg, while the Earth's mass is m = 6 x 10^24 kg, with a distance of R = 1.5 x 10^11 m separating them. Applying Newton's law for gravitational force F = G (mM / R²), where G = 6.67 × 10^-11 m^3 kg^-1 s^-2 gives us F = 3.56 x 10^22 N. A) The gravitational force by the sun on Earth equates to the force exerted by Earth on the sun, which is also 3.56 x 10^22 N.
7 0
1 month ago
Heating a metal from room temperature to pouring temperature in a casting operation depends on all of the following properties e
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Response:

(e) thermal expansion

Clarification:

The density, heat of fusion, and melting temperature of a metal are critical factors to consider when increasing its temperature from room temperature to its melting point. These will dictate the following aspects:

Density: refers to the ratio between a body's mass and the space it occupies in the universe.

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7 0
21 day ago
A sphere of radius 0.03m has a point charge of q= 7.6 micro C located at it’s centre. Find the electric flux through it?
Sav [3153]

Answer:

The electric flux going through the sphere is 8.58 *10^{5} \frac{Nm^2}{C}

Explanation:

Given

Radius,\ r = 0.03m\\Charge,\ q =7.6\µC

Required

Calculate the electric flux

Electric flux can be computed using the formula;

Ф = q/ε

Where ε stands for the electric constant permittivity

ε = 8.8542 * 10^{-12}

Substituting ε = 8.8542 * 10^{-12} and q =7.6\µC; the formula simplifies to

Ф = \frac{7.6\µC}{8.8542 * 10^{-12}}

Ф = \frac{7.6 * 10^{-6}}{8.8542 * 10^{-12}}

Ф = \frac{7.6}{8.8542} *\frac{10^{-6}}{10^{-12}}

Ф = \frac{7.6}{8.8542} *10^{12-6}}

Ф = 0.85834970974 *10^{12-6}}

Ф = 0.85834970974 *10^{6}}

Ф = 8.5834970974 *10^{5}}

Ф = 8.58 *10^{5} \frac{Nm^2}{C}

Thus, the electric flux through the sphere is 8.58 *10^{5} \frac{Nm^2}{C}

7 0
2 months ago
Vehicle crumple zones are designed to absorb energy during an impact by deforming to reduce energy transfer to the occupants. Ho
kicyunya [3294]

Answer:

change in KE = -12.95 Btu

Explanation:

provided data

mass = 3000-lbm

initial velocity of vehicle vi = 10 mph = 14ft/s

final velocity of vehicle vf = 0 mph = 0 ft/s

solution

the crumple zone is designed to absorb kinetic energy upon impact

thus the change in KE is related to the initial and final speeds, expressed as:

change in KE = 0.5 × m × (vf² - vi² ).................1

Substituting in the parameters yields:

change in KE = 0.5 × 3000 × (0² - 14.7² )

change in KE = -324135 × \frac{1lbf}{32.174\ lb.ft/s^2} * \frac{1Btu}{778.17 ft.lbf}  

change in KE = -12.95 Btu

5 0
1 month ago
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serg [3582]

Answer:The tension on either side of the cable is 3677.57 N

Explanation:

given data

traffic light = 20 kg

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sag of the cable = 0.40 m

solution

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tan θ = \frac{0.4}{15}.............1

θ = 1.527 °

and

tension = mg

The horizontal net force can be stated as

T2 cosθ = T1 cosθ.................2

and

thus T2 - T1..............3

and

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7 0
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