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Salsk061 [2.6K]

1 year ago

7

An LR circuit contains an ideal 60-V battery, a 42-H inductor having no resistance, a 24-ΩΩ resistor, and a switch S, all in ser

ies. Initially, the switch is open and has been open for a very long time. At time t = 0 s, the switch is suddenly closed. How long after closing the switch will the potential difference across the inductor be 24 V?

1 answer:

s2008m [1.1K]1 year ago

3 0

Answer:

1.6 s

Explanation:

To find the time in which the potential difference of the inductor reaches 24V you use the following formula:

$V_L=V_oe^{-\frac{Rt}{L}}$

V_o: initial voltage = 60V

R: resistance = 24-Ω

L: inductance = 42H

V_L: final voltage = 24 V

You first use properties of the logarithms to get time t, next, replace the values of the parameter:

$\frac{V_L}{V_o}=e^{-\frac{Rt}{L}}\\\\ln(\frac{V_L}{V_o})=-\frac{Rt}{L}\\\\t=-\frac{L}{R}ln(\frac{V_L}{V_o})\\\\t=-\frac{42H}{24\Omega}ln(\frac{24V}{60V})=1.6s$

hence, after 1.6s the inductor will have a potential difference of 24V

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The temperature, T, of a gas is jointly proportional to the pressure P of the gas and the volume V occupied by the gas. Use C as

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Answer:

T=C*P*V

Explanation:

It is said that a variable - let's call 'y' -, is proportional to another - let's call it 'x' - if x and y are multiplicatively connected to a constant 'C'. It means that their product (x*y) can be always equaled to the constant 'C' or their division ( $\frac{x}{y}$ ) can be always equaled to 'C'. The first case is the case of the inverse proportionality: It is said that x and y are inversely proportional if

$x*y=C$

The second case is the case of the direct proportionality: It is said that x and y are directly proportional if

$\frac{x}{y} =C$ : x is directly proportional to y.

or

$\frac{y}{x} =C$ : y is directly proportional to x.

Always that any text does not specify about directly or inversely proportionality, it is assumed to mean directly automatically.

For our case, we are said that the temperature T is proportional to the pressure P and the volume V (we assume that it means directly); it is a double proportionality but follows the same rules:

If T were just proportional to P, we would have:

$\frac{T}{P} =C$

If T were just proportional to V, we would have:

$\frac{T}{V} =C$

As T is proportional to both P and V, the right equation is:

$\frac{T}{P*V}=C$

In order to isolate the temperature, let's multiply (P*V) at each side of the equation:

$\frac{T}{P*V}*(P*V)=C*(P*V)\\T=C*P*V$

3 0

1 year ago

A car hits another and the two bumpers lock together during the collision. is this an elastic or inelastic collision?

valkas [14]

Inelastic.
If it was elastic, they'd bump right off each other. But since they've been locked, or stuck together, this is inelastic.

8 0

2 years ago

The length of a 60 W, 240 Ω light bulb filament is 60 cm Remembering that the current in the filament is proportional to the ele

faust18 [17]

Answer:

Finally current will be

i = 0.35 A

Explanation:

As we know that power of the bulb is given by the formula

$P = \frac{V^2}{R}$

now we have

$P = 60 W$

R = 240 ohm

so we have

$60 = \frac{V^2}{240}$

$V = 120 Volts$

now the current in the bulb is given as

$i = \frac{V}{R}$

$i = \frac{120}{240} = 0.5 A$

now when length of the filament is double

so the resistance of the wire also gets double

so we have

$P = \frac{V^2}{R}$

$60 = \frac{V^2}{480}$

$V = 169.7 volts$

now the current in the bulb is given as

$V = i R$

$169.7 = i(480)$

$i = 0.35 A$

8 0

1 year ago

Estimate the change in the equilibrium melting point of copper caused by a change in pressure of 10 kbar. The molar volume of co

mr Goodwill [35]

Answer:

The change in the equilibrium melting point is 4.162 K.

Explanation:

Given that,

Pressure = 10 kbar

Molar volume of copper $V=8.0\times10^{-6}\ m^3$

Volume of liquid $V=7.6\times10^{-6}\ m^3$

Latent heat of fusion $L= 13.05 kJ$

Melting point =1085°C

We need to calculate the change temperature

Using Clapeyron equation

$\dfrac{\Delta P}{\Delta T}=\dfrac{\Delta H}{T\Delta V}$

Put the value into the formula

$\dfrac{1000\times10^{5}}{\Delta T}=\dfrac{13050}{(1085+273)\times(8.0-7.6)\times10^{-6}}$

$\Delta T=\dfrac{1000\times10^{-5}\times(1085+273)\times(8.0-7.6)\times10^{-6}}{13050}$

$\Delta T=4.162\ K$

Hence, The change in the equilibrium melting point is 4.162 K.

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1 year ago

In a 5000 m race, the athletes run 12 1/2 laps; each lap is 400 m.Kara runs the race at a constant pace and finishes in 17.9 min

Ksju [112]

Answer:

No. of laps of Hannah are 7 (approx).

Solution:

According to the question:

The total distance to be covered, D = 5000 m

The distance for each lap, x = 400 m

Time taken by Kara, $t_{K} = 17.9 min = 17.9\times 60 = 1074 s$

Time taken by Hannah, $t_{H} = 15.3 min = 15.3\times 60 = 918 s$

Now, the speed of Kara and Hannah can be calculated respectively as:

$v_{K} = \frac{D}{t_{K}} = \frac{5000}{1074} = 4.65 m/s$

$v_{H} = \frac{D}{t_{H}} = \frac{5000}{918} = 5.45 m/s$

Time taken in each lap is given by:

$(v_{H} - v_{K})t = x$

$(5.45 - 4.65)\times t = 400$

$t = \frac{400}{0.8}$

t = 500 s

So, Distance covered by Hannah in 't' sec is given by:

$d_{H} = v_{H}\times t$

$d_{H} = 5.45\times 500 = 2725 m$

No. of laps taken by Hannah when she passes Kara:

$n_{H} = \frac{d_{H}}{x}$

$n_{H} = \frac{2725}{400} = 6.8$ ≈ 7 laps

3 0

1 year ago