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Class 12th Physics Alternating Current

An inductor of 0.5 mH, a capacitor of 200 $μ F$ and a resistor of 2 $Ω$ are connected in series with a 220V ac source. If the current is in phase with the emf, the frequency of ac source will be__________ * 10² Hz.

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Payal Gupta

Contributor-Level 10

Since current is in phase with voltage, it means circuit is in resonance, so we can write

f = $\frac{1}{2 π \sqrt[]{L C}} = \frac{1}{2 π \sqrt[]{(0.5 * 1 0^{- 3}) * (200 * 1 0^{- 6})}}$

$\Rightarrow f = \frac{1 0^{4}}{2 π \sqrt[]{10}} \approx 5 * 1 0^{2} H z$ $[T a k i n g π = \sqrt[]{10}]$

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New answer posted

a year ago

Class 12th Physics Wave Optics

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by 5 * 10^-²m towards the slits, the change in fringe width is 3 * 10^-³cm. If the distance between the slits is 1mm, then the wavelength of the light will be_____________ nm.

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Payal Gupta

Contributor-Level 10

According to Young's double slit experiment, we can write

$β = \frac{λ D}{d} \Rightarrow Δ β = β_{2} - β_{1} = \frac{λ}{d} Δ D$

$\Rightarrow λ = \frac{d Δ β}{Δ D} = \frac{1 * 1 0^{- 3} * 3 * 1 0^{- 5}}{5 * 1 0^{- 2}} = 60 * 1 0^{- 8} m = 600 n m$

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New answer posted

a year ago

Class 12th Physics Nuclei

The half life of a radioactive substance is 5 years. After x years a given sample of the radioactive substance gets reduced to 6/25% of its initial value. The value of x is___________.

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Payal Gupta

Contributor-Level 10

According to Nuclear activity, we can write

$N_{0} \overset{t_{\frac{1}{2}}}{\to} \frac{N_{0}}{2} \overset{t_{\frac{1}{2}}}{\to} \frac{N_{0}}{4} \overset{t_{\frac{1}{2}}}{\to} \frac{N_{0}}{8} \overset{t_{\frac{1}{2}}}{\to} \frac{N_{0}}{16} = (0.0625) N_{0}$

Time required = 4 * $t_{\frac{1}{2}} = 20 y r s$

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New answer posted

a year ago

Class 12th Physics

The displacement current of 4.425 $μ A$ is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 10⁶ Vs^-¹. The area of each plate of the capacitor is 40 cm². The distance between each plate of the capacitor is x * 10^-³. The value of x is,

(Permittivity of free space, $E_{0} = 8.85 * 1 0^{- 12} C^{2} N^{- 1} m^{- 2})__________$

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Payal Gupta

Contributor-Level 10

According to definition of displacement current, we can write

$I_{d} = ε_{0} \frac{d ?}{d t} = ε_{0} \frac{d (E S)}{d t} = ε_{0} \frac{d (\frac{V}{l} S)}{d t} = \frac{ε_{0} S}{l} (\frac{d V}{d t})$

$\Rightarrow l = \frac{8.85 * 1 0^{- 12} * 40 * 1 0^{- 4} * 1 0^{6}}{4.425 * 1 0^{- 6}} 8 * 1 0^{- 3} m$

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New answer posted

a year ago

Class 12th Physics

A potential barrier of 0.4V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 * 10⁵. The speed with which electron enters the p side will be $\frac{x}{3} * 1 0^{5} m s^{- 1}$ the value of x is__________.

(Given mass of electron = 9 * 10^-³¹ kg, charge on electron = 1.6 * 10^-¹⁹ C.)

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Payal Gupta

Contributor-Level 10

According to Work energy theorem, we can write

$K_{f} - K_{i} = W_{E l e c t r i c F o r c e} \Rightarrow \frac{1}{2} m v^{2} - \frac{1}{2} m v_{0}^{2} = - e V \Rightarrow v^{2} = v_{0}^{2} - \frac{2 e V}{m}$

$\Rightarrow v^{2} = {(6.0 * 1 0^{5})}^{2} - \frac{2 * 1.6 * 1 0^{- 19}}{9 * 1 0^{- 31}} = \frac{324 - 128}{9} * 1 0^{10} = \frac{196}{9} * 1 0^{10} \Rightarrow V = \frac{14}{3} * 1 0^{5} m / s$

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New answer posted

a year ago

Class 12th Physics

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 $Ω$ is used to measure the potential difference across 500 $Ω$ resister, the reading of the voltmeter will be_________ V.

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Payal Gupta

Contributor-Level 10

According to Kirchhoff's Law, we can write

20 + 2000I + 600 * 5I = 0 $\Rightarrow I = \frac{20}{5000} A$

Reading of voltmeter = 2000I = 2000 * $\frac{20}{5000} = 8 v o l t$

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New answer posted

a year ago

Class 12th Physics

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of $2 Ω .$ The value of internal resistance of each cell is

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Payal Gupta

Contributor-Level 10

According to question, we can write

$\frac{2 V}{2 + 2 r} = \frac{V}{2 + \frac{r}{2}}$

$\Rightarrow 2 + 2 r = 4 + r \Rightarrow r = 2 Ω$

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New answer posted

a year ago

Class 12th Physics Electric Charge and Field

If the electric potential at any point (x, y, z)m in space is given by V = 3x² volt. The electric field at the point (1, 0, 3)m will be

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Payal Gupta

Contributor-Level 10

According to relation between field and potential, we can write

$\vec{E} = - \frac{d V}{d x} (\hat{i}) = - \frac{d (3 x^{2})}{d x} (\hat{i}) = - 6 x (\hat{i})$

${\vec{E}}_{(1, 0, 3)} = - 6 (\hat{i}) N / C$

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