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Andrej [43]
3 years ago
9

Two capacitors of capacitances 25 µF and 50 µF are connected in series with a 33-V battery. How much energy is stored in the 25-

µF capacitor when it is fully charged?
Physics
1 answer:
torisob [31]3 years ago
5 0

Answer:

6.05×10⁻³ J

Explanation:

Note: Two capacitors connected in series behaves like two resistors connected in parallel.

Using

1/Ct = 1/C1+1/C2

Ct = (C1×C2)/(C1+C2)............................ Equation 1

Where Ct = combined capacitance of the two capacitor, C1 = Capacitance of the first capacitor, C2 = capacitance of the second capacitor.

Given: C1 = 25 µF, C2 = 50 µF

Substitute into equation 1

Ct = (25×50)/(25+50)

Ct = 1250/75

Ct = 16.67 µF.

Using

Q = CV.................... Equation 2

Where Q = Charge, V = Voltage.

Given: V = 33 V, C = 16.67 µF = 16.67×10⁻⁶ F

Substitute into equation 2

Q = 33(16.67×10⁻⁶)

Q = 5.5×10⁻⁴ C.

Since both capacitors are connected in series, the same amount of charge flows through them.

Using,

E = 1/2Q²/C.................. Equation 3

Where E = Energy stored in the 25-µF capacitor

Given: Q =5.5×10⁻⁴ C, C = 25 µF = 25×10⁻⁶ F

Substitute into equation 3

E = 1/2(5.5×10⁻⁴)²/ 25×10⁻⁶

E = 6.05×10⁻³ J.

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Two traveling sinusoidal waves are described by the wave functions y1 = 4.85 sin [(4.35x − 1270t)] y2 = 4.85 sin [(4.35x − 1270t
Tamiku [17]

Answer:

Approximately 9.62.

Explanation:

y_1 = 4.85\, \sin[(4.35\, x - 1270\, t) + 0].

y_2 = 4.85\, \sin[(4.35\, x - 1270\, t) + (-0.250)].

Notice that sine waves y_1 and y_2 share the same frequency and wavelength. The only distinction between these two waves is the (-0.250) in y_2\!.

Therefore, the sum (y_1 + y_2) would still be a sine wave. The amplitude of (y_1 + y_2)\! could be found without using calculus.

Consider the sum-of-angle identity for sine:

\sin(a + b) = \sin(a) \cdot \cos(b) + \cos(a) \cdot \sin(b).

Compare the expression \sin(a + b) to y_2. Let a = (4.35\, x - 1270) and b = (-0.250). Apply the sum-of-angle identity of sine to rewrite y_2\!.

\begin{aligned}y_2 &= 4.85\, \sin[(\underbrace{4.35\, x - 1270\, t}_{a}) + (\underbrace{-0.250}_{b})]\\ &= 4.85 \, [\sin(4.35\, x - 1270\, t)\cdot \cos(-0.250) \\ &\quad\quad\quad\; + \cos(4.35\, x - 1270\, t)\cdot \sin(-0.250)] \end{aligned}.

Therefore, the sum (y_1 + y_2) would become:

\begin{aligned}& y_1 + y_2\\[0.5em] &= 4.85\, [\sin(4.35\, x - 1270\, t) \\ &\quad \quad \quad\;+\sin(4.35\, x - 1270\, t)\cdot \cos(-0.250) \\ &\quad\quad\quad\; + \cos(4.35\, x - 1270\, t)\cdot \sin(-0.250)] \\[0.5em] &= 4.85\, [\sin(4.35\, x - 1270\, t)\cdot (1 + \cos(-0.250)) \\ &\quad\quad\quad\; + \cos(4.35\, x - 1270\, t)\cdot \sin(-0.250)] \end{aligned}.

Consider: would it be possible to find m and c that satisfy the following hypothetical equation?

\begin{aligned}& (4.85\, m)\cdot \sin((4.35\, x - 1270\, t) + c)\\&= 4.85\, [\sin(4.35\, x - 1270\, t)\cdot (1 + \cos(-0.250)) \\ &\quad\quad\quad\; + \cos(4.35\, x - 1270\, t)\cdot \sin(-0.250)] \end{aligned}.

Simplify this hypothetical equation:

\begin{aligned}& m\cdot \sin((4.35\, x - 1270\, t) + c)\\&=\sin(4.35\, x - 1270\, t)\cdot (1 + \cos(-0.250)) \\ &\quad\quad + \cos(4.35\, x - 1270\, t)\cdot \sin(-0.250)\end{aligned}.

Apply the sum-of-angle identity of sine to rewrite the left-hand side:

\begin{aligned}& m\cdot \sin((4.35\, x - 1270\, t) + c)\\[0.5em]&=m\, \sin(4.35\, x - 1270\, t)\cdot \cos(c) \\ &\quad\quad + m\, \cos(4.35\, x - 1270\, t)\cdot \sin(c) \\[0.5em] &=\sin(4.35\, x - 1270\, t)\cdot (m\, \cos(c)) \\ &\quad\quad + \cos(4.35\, x - 1270\, t)\cdot (m\, \sin(c)) \end{aligned}.

Compare this expression with the right-hand side. For this hypothetical equation to hold for all real x and t, the following should be satisfied:

\displaystyle 1 + \cos(-0.250) = m\, \cos(c), and

\displaystyle \sin(-0.250) = m\, \sin(c).

Consider the Pythagorean identity. For any real number a:

{\left(\sin(a)\right)}^{2} + {\left(\cos(a)\right)}^{2} = 1^2.

Make use of the Pythagorean identity to solve this system of equations for m. Square both sides of both equations:

\displaystyle 1 + 2\, \cos(-0.250) +  {\left(\cos(-0.250)\right)}^2= m^2\, {\left(\cos(c)\right)}^2.

\displaystyle {\left(\sin(-0.250)\right)}^{2} = m^2\, {\left(\sin(c)\right)}^2.

Take the sum of these two equations.

Left-hand side:

\begin{aligned}& 1 + 2\, \cos(-0.250) + \underbrace{{\left(\cos(-0.250)\right)}^2 + {\left(\sin(-0.250)\right)}^2}_{1}\\ &= 1 + 2\, \cos(-0.250) + 1 \\ &= 2 + 2\, \cos(-0.250) \end{aligned}.

Right-hand side:

\begin{aligned} &m^2\, {\left(\cos(c)\right)}^2 + m^2\, {\left(\sin(c)\right)}^2 \\ &= m^2\, \left( {\left(\sin(c)\right)}^2 +  {\left(\cos(c)\right)}^2\right)\\ &= m^2\end{aligned}.

Therefore:

m^2 = 2 + 2\, \cos(-0.250).

m = \sqrt{2 + 2\, \cos(-0.250)} \approx 1.98.

Substitute m = \sqrt{2 + 2\, \cos(-0.250)} back to the system to find c. However, notice that the exact value of c\! isn't required for finding the amplitude of (y_1 + y_2) = (4.85\, m)\cdot \sin((4.35\, x - 1270\, t) + c).

(Side note: one possible value of c is \displaystyle \arccos\left(\frac{1 + \cos(0.250)}{\sqrt{2 \times (1 + \cos(0.250))}}\right) \approx 0.125 radians.)

As long as \! c is a real number, the amplitude of (y_1 + y_2) = (4.85\, m)\cdot \sin((4.35\, x - 1270\, t) + c) would be equal to the absolute value of (4.85\, m).

Therefore, the amplitude of (y_1 + y_2) would be:

\begin{aligned}|4.85\, m| &= 4.85 \times \sqrt{2 + 2\, \cos(-0.250)} \\&\approx 9.62 \end{aligned}.

8 0
3 years ago
Static, sliding and rolling are types of friction true or false
Marina CMI [18]
True because friction happens when two things are rubbed against each other and it creates force and sliding something vigorously against something else can create force.
4 0
3 years ago
Read 2 more answers
Please help on this one somebody?
coldgirl [10]

7.5 x 10⁻¹¹m. An electromagnetic wave of frecuency 4.0 x 10¹⁸Hz has a wavelength of 7.5 x 10⁻¹¹m.

Wavelength is the distance traveled by a periodic disturbance that propagates through a medium in a certain time interval. The wavelength, also known as the space period, is the inverse of the frequency. The wavelength is usually represented by the Greek letter λ.

λ = v/f. Where v is the speed of propagation of the wave, and "f" is the frequency.

An electromagnetic wave has a frecuency of 4.0 x 10 ¹⁸Hz and the speed of light is 3.0 x 10⁸ m/s. So:

λ = (3.0 x 10⁸ m/s)/(4.0 x 10¹⁸ Hz)

λ = 7.5 x 10⁻¹¹m

8 0
3 years ago
An object weighs 32 newtons. What is its mass if a gravitometer indicates that g = 8.25 m/s?
Elan Coil [88]

Explanation:

weight=mass×g

32=mass×8.25

mass=

\frac{128}{33}  = 3.878kg

8 0
2 years ago
When water freezes, its volume increases by 9.05%. What force per unit area is water capable of exerting on a container when it
AnnZ [28]

Answer:

The Pressure is 0.20 MPa.

(b) is correct option.

Explanation:

Given that,

Change in volume = 9.05%

{tex]\dfrac{\Delta V}{V_{0}}=0.0905[/tex]

We know that.

The bulk modulus for water

B=0.20\times10^{10}\ N/m^2

We need to calculate the pressure difference

Using formula bulk modulus formula

B=\Delta P\dfrac{V_{0}}{\Delta V}

\Delta P=B\dfrac{\Delta V}{V_{0}}

\Delta P=0.2\times10^{10}\times0.0905

\Delta P=0.2\times10^{6}\ Pa

\Delta P=0.20 MPa

Hence, The Pressure is 0.20 MPa.

6 0
3 years ago
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