A flight into space by a spacecraft where the spacecraft returns to Earth without achieving orbit is called a

A television channel is assigned the frequency range from 54 MHz to 60 MHz. A series RLC tuning circuit in a TV receiver resonat

Stella [2.4K]

Answer:

A.) L = 0.37 μH B) 7.61 Ω

Explanation:

A) At resonance, the circuit behaves like it were purely resistive , so the reactance value must be 0.

So, the following condition must be met:

ω₀*L = 1/ (ω₀*C) ⇒ ω₀² = 1/LC

We know that, for a sinusoidal source, there exists a fixed relationship between the angular frequency ω₀ and the frequency f₀, as follows:

ω₀ = 2*π*f₀

⇒ (2*π*f₀)² = 1/(L*C)

Replacing by the givens (f₀, C), we can solve for L:

L = 1 /((2*π*f₀)²*C) = 1/(2*π*57*10⁶)² Hz²*21*10⁻¹² f = 0.37 μH

b) At resonance, the current can be expressed as follows:

I₀ = V/Z = V/R

We need to find the minimum value of R that satisfies the following equation:

I = 0.5 I₀ = 0.5 V/R = V/Z

⇒ 0.5/R = 1/√(R²+X²)

Squaring both sides , we have:

(0.5)²/R² = 1/ (R²+X²)

⇒ 0.25 (R²+X²) = R² ⇒ R² = X² / 3

We need to find the value of R that satisfies the requested condition througout the frequency range.

So, we need to find out the value of the reactance X in the lowest and highest frequency, as follows:

Xlow = ωlow * L - 1/(ωlow*C)

⇒ Xlow = ( (2*π*54*10⁶)*0.37*10⁻⁶) - 1/ ((2*π*54*10⁶)*21*10⁻¹²) = -14.81Ω

Xhi = ωhi * L - 1/(ωhi*C)

⇒ Xhi = ( (2*π*60*10⁶)*0.37*10⁻⁶) - 1/ ((2*π*60*10⁶)*21*10⁻¹²) = 13.18Ω

For these reactance values, we can find the corresponding values of R as follows:

Rlow² = Xlow²/3 = (-14.81)²/3 = 75Ω² ⇒ Rlow = 8.55 Ω

Rhi² = Xhi² / 3 = (13.18)²/3 = 56.33Ω² ⇒Rhi = 7.61 Ω

The minimum value of R that satisfies the requested condition is R= 7.61ΩΩ.

3 0

3 years ago

A series RLC circuit has a resistance of 57.61 W, a capacitance of 13.13 mF, and an inductance of 196.03 mH. The circuit is conn

Firdavs [7]

Answer:

voltage across = 1.6 V

Explanation:

given data

resistance R = 57.61 Ω

capacitance c = 13.13 mF = 13.13 × $10^{-3}$ F

inductance L = 196.03 mH = 0.19603 H

fixed rms output Vrms = 23.86 V

to find out

voltage across circuit

solution

we know resonant frequency that is

resonant frequency = 1 / ( 2π√(LC)

put the value

resonant frequency = 1 / ( 2π√(0.19603×13.13 × $10^{-3}$ )

resonant frequency f = 3.1370 HZ

so current will be at this resonant is

current = Vrms / R

current = 23.86 / 57.61

current = 0.4141 A

and

so voltage across will be

voltage across = current / ( 2π f C )

voltage across = 0.4141 / ( 2π ( 3.1370) 13.13 × $10^{-3}$ )

voltage across = 1.6 V

4 0

3 years ago

What will happen to the astronaut when the jets produce these four forces: 10N, 10N, 9N, 9N?

sukhopar [10]

The astronaut would go the opposite direction due to Newton’s third law of -10N, -10N, -9N, -9N

Let me know if this helped you, please rank this was the brainlist answer if possible, thanks!

6 0

4 years ago

Air enters a 28-cm diameter pipe steadily at 200 kPa and 20°C with a velocity of 5 m/s. Air is heated as it flows and leaves the

abruzzese [7]

Answer:

The mass flow rate of air is 0.732 kg/s.

The velocity at the exit is 5.927 m/s.

Explanation:

Given that,

Diameter = 28 cm

Enter pressure= 200 kPa

Enter temperature = 20°C

Velocity = 5 m/s

Exit pressure = 180 kPa

Exit temperature = 40°C

We need to calculate the mass flow rate of air

Using formula of mass flow rate

$\dot{m}=\rho\times \dot{V}$

$\dot{m}=\dfrac{P}{RT}\times A\times v$

Put the value into the formula

$\dot{m}=\dfrac{200}{0.287\times293}\times\dfrac{(0.28)^2}{4}\times\pi\times5$

$\dot{m}=0.732\ kg/s$

We need to calculate the volume flow rate

Using formula of volume flow rate

$\dot{V'}=\dfrac{\dot{m}}{\rho'}$

$\dot{V'}=\dfrac{RT'\dot{m}}{P'}$

$\dot{V'}=\dfrac{0.287\times313\times0.732}{180}$

$\dot{V'}=0.365\ m^3/s$

We need to calculate the velocity at the exit

Using formula of velocity

$v'=\dfrac{\dot{V'}}{A}$

Put the value into the formula

$v'=\dfrac{4\times0.365}{(0.28)^2\times\pi}$

$v'=5.927\ m/s$

Hence, The mass flow rate of air is 0.732 kg/s.

The velocity at the exit is 5.927 m/s.

4 0

3 years ago

If f(x)=5x+40, what is f(x) when x =-5?

LuckyWell [14K]

Answer:

<h3>given</h3>

- x = (-5)

To find - Value of the equation

Solution -

5x + 40

Putting value of x = (-5) in equation

5(-5) + 40

-25 + 40

15

7 0

3 years ago

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