Electromagnetic Induction

A capacitor of capacitance 500 $μ F$ is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. Then maximum current in LC circuit will be_______ A.

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Contributor-Level 10

C = 500 $μ F,$ V = 100 v, L = 50 mH

In this LC – oscillation

q = q₀ cos $ω t$

$i = \frac{- d q}{d t} = q_{0} ω s i n ω t ω = \frac{1}{\sqrt[]{2 c}} = \frac{1}{\sqrt[]{50 * 1 0^{- 3} * 5 * 1 0^{- 4}}}$

= $\frac{1000}{5} = 200$

So, i_max = $q_{0} ω = 500 * 1 0^{6} * 100 * 200$

= 10A

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2 months ago

A conducting circular loop is placed in X – Y plane in presence of magnetic field $\vec{B} = (3 t^{3} \hat{j} + 3 t^{2} \hat{k})$ in SI unit. If the radius of the loop is 1m. The induced emf in the loop, at time, t = 2s is npV. The value of n is__________.

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Vishal Baghel

Contributor-Level 10

$? = \vec{B} . \vec{A}$

$= (3 t^{3} \hat{j} + 3 t^{2} \hat{k}) . (π {(1)}^{2} \hat{k})$

$? = 3 t^{2} π$

$E_{i n d} = | \frac{d ?}{d t} | = 6 t π$

at t = 2, E_ind = 12

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2 months ago

Magnetic flux (in weber) in a closed circuit of resistance $20 Ω$ varies with time t(s) as $?$ = 8t² – 9t + 5. The magnitude of the induced current at t = 0.25s will be _______mA.

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Contributor-Level 10

$e_{i n} = | \frac{d ?}{d t} | = | 16 t - 9 | e_{i n} = | 16 * \frac{1}{4} - 9 | = 5 v o l t$

$l = \frac{e_{i n}}{R} = \frac{5}{20} A = \frac{5}{20} * 1000 m A = 250 m A$

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2 months ago

A capacitor of capacitance 500 $μ F$ is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. Then maximum current in LC circuit will be_______ A.

0 Follower 2 Views

Contributor-Level 10

C = 500 $μ F,$ V = 100 v, L = 50 mH

In this LC – oscillation

q = q₀ cos $ω t$

$i = \frac{- d q}{d t} = q_{0} ω s i n ω t ω = \frac{1}{\sqrt[]{2 c}} = \frac{1}{\sqrt[]{50 * 1 0^{- 3} * 5 * 1 0^{- 4}}}$

= $\frac{1000}{5} = 200$

So, i_max = $q_{0} ω = 500 * 1 0^{6} * 100 * 200$

= 10A

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New answer posted

2 months ago

The current in a coil of self inductance 2.0 H is increasing according to I = 2sin(t²)A. The amount of energy spent during the period when current changes from 0 to 2 A is…………J.

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Contributor-Level 10

Given, L = 2H

l = 2 sin (t²)

$u = \int_{0}^{2} L i d i = \frac{L}{2} {[i^{2}]}_{0}^{2} = \frac{L}{2} [4 - 0]$

$u = \frac{2}{2} * 4 = 4 J$

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2 months ago

A circular coil of 1000 turns each with area 1m² is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07 T. The maximum voltage generation will be ________V.

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Contributor-Level 10

given N = 1000 turns

A = 1m²

$ω = 1 r e v / s e c$

$= 1 * 2 π r a d / s e c$

$V = \frac{- d ?_{B}}{d t} = \frac{- d}{d t} (N B A c o s ω t)$

= $140 * \frac{22}{7}$

= 20 * 22

= 440 volts

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2 months ago

All resistances in figure are $1 Ω$ each. The value of current 'I' is $\frac{a}{5} A .$ The value of a is___________.

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Contributor-Level 10

I = $\frac{3 * 8}{15 R} = \frac{8}{5 R} = \frac{a}{5}$

$\Rightarrow \frac{8}{5 * 1} = \frac{a}{5}$

a = 8

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2 months ago

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be:

(Assume the coil to be short circuited.)

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Electromagnetic Induction Physics NCERT Exemplar Solutions Class 12th Chapter Six

Contributor-Level 10

$P = \frac{E^{2}}{R} = \frac{{(N A \frac{d B}{d t})}^{2} * 4 A C}{ρ l}$

$p' = {(\frac{N A}{2} \frac{d B}{d t})}^{2} * 4 A C$

$p' = 2 P$

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2 months ago

A small bar magnet is moved through a coil at constant speed from one end to the other. Which of the following series of observations will be seen on the galvanometer G attached across the coil?

Three positions shown describe:

(a) The magnet's entry

(b) Magnet is completely inside and

(c) Magnet's exit

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Electromagnetic Induction Physics NCERT Exemplar Solutions Class 12th Chapter Six

Contributor-Level 10

Kindly go through the solution

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2 months ago

A air bubble of radius 1 cm in water has an upward acceleration 9.8 cm^-2 . The density of water is 1 gmcm^-3 and water offers negligible drag force on the bubble. The mass of the bubble is: (g=980 cm/s²)

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