Class 12th

Contributor-Level 10

As charge remains same. So,
Initial total charge Q = (2C)V + CV = 3CV
When dielectric is inserted in C, its new capacitance is KC.
The capacitors 2C and KC are in parallel.
Equivalent capacitance C_eq = 2C + KC = (K+2)C
New potential Vc = Q/C_eq = 3CV/ (K+2)C) = 3V/ (K+2)

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a year ago

Class 12th Atoms

If 'f' denotes the ratio of the number of nuclei decayed (Nd) to the number of nuclei at t = 0 (N?) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as: [λ is the radioactive decay constant]

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Class 12th Physics Ncert Solutions Class 12th

Contributor-Level 10

f = (N? - N? (e? )/N?
f = 1 - e?
df/dt = 0 - e? * -λ = λe?

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New answer posted

a year ago

Identify the logic operation carried out.
(The diagram shows a logic circuit with two inputs A and B. Both A and B are inputs to a NAND gate. The output of this NAND gate is then fed into both inputs of a second NAND gate, which produces the final output Y.)

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Class 12th Physics Wave Optics

Contributor-Level 9

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a year ago

The relative permittivity of distilled water is 81. The velocity of light in it will be: (Given µ? = 1)

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Class 12th Dual Nature of Radiation and Matter

Contributor-Level 10

v = 1/√με = 1/√ (µ? µ? ε? ε? ) = c/√ (µ? ε? )
v = 3*10? / √ (1*81)
v = 3*10? / 9 m/s
= 0.33 * 10? m/s
= 3.33 * 10? m/s

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a year ago

A particle of mass 4M at rest disintegrates into two particles of mass M and 3M respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass M to that of mass 3M will be :

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Class 12th Physics Electrostatic Potential and Capacitance

Contributor-Level 9

MV? = 3MV? = p
λ = h/mv = h/p
λ? /λ? = 1

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a year ago

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be: (Given area of plate = A)

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Contributor-Level 10

1/Ceq = 1/C? + 1/C? + 1/C?
1/Ceq = 1/ (K Aε? /d) + 1/ (3K Aε? /2d) + 1/ (5K Aε? /3d)
1/Ceq = d/ (K Aε? ) + 2d/ (3K Aε? ) + 3d/ (5K Aε? )
1/Ceq = (d/K Aε? ) * (1 + 2/3 + 3/5)
1/Ceq = (d/K Aε? ) * (15+10+9)/15) = 34d / (15K Aε? )
Ceq = 15K Aε? / 34d

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a year ago

The half-life of ¹?Au is 3 days. If atomic weight of ¹?Au is 198 g/mol then the activity of 2 mg of ¹?Au is [ in disintegration / second ] :

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Contributor-Level 9

t? /? = 3 days = 72 hours
dN/dt = λN = (ln2/t? /? ) N
= (0.693 * 6.02*10²³ * 2*10? ³) / (72 * 3600 * 198)
= 1.618 * 10¹³
= 16.18 * 10¹² disintegration/second

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a year ago

A capacitor of capacitance C = 1µF is suddenly connected to a battery of 100 volt through a resistance R = 100Ω. The time taken for the capacitor to be charged to get 50 V is: [Take ln 2 = 0.69]

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Contributor-Level 10

V = E (1 - e? /τ)
Where τ = RC = 100 * 10? = 10? sec
50V = 100V (1 - e? /10? )
1/2 = 1 - e? ¹?
1/2 = e? ¹?
-ln2 = -10? t
t = ln2/10?
t = 0.693 * 10? sec

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New answer posted

a year ago

A parallel plate capacitor with plate area 'A' and distance of separation 'd' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as

ε(x) = ε? + kx, for 0 < x d/2
ε(x) = ε? + k(d-x), for d/2 ≤ x ≤ d

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Contributor-Level 9

dC? = (ε? + kx)A / dx [For 0 < x < d/2]
1/C? = ∫ dx / (ε? + kx)A) from 0 to d/2
= (1/Ak) [ln (ε? + kx)] from 0 to d/2
= (1/kA) ln (1 + kd/ (2ε? )
C? = kA / ln (1 + kd/ (2ε? )

Similarly dC? = (ε? + k (d-x)A / dx [For d/2 ≤ x ≤ d]
C? = kA / ln (1 + kd/ (2ε? )
Clearly, C? = C? = C
For series combination:
C_eq = C? / (C? + C? ) = C/2 = kA / (2ln (2ε? + kd)/2ε? )

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New answer posted

a year ago

In the given figure, a battery of emf E is connected across a conductor PQ of length 'l' and different area of cross- sections by having radii r? and r? (r? < r?). Choose the correct option as one moves from P to Q:

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