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Partially Filled Dielectrics

In the given ...

Question

In the given circuit, the steady state voltage drop
across the capacitor C is

\frac{V r_{1}}{r_{2} + r_{3}}

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\frac{V r_{2}}{r_{1} + r_{3}}

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\frac{V r_{1}}{r_{1} + r_{2}}

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\frac{V r_{2}}{r_{1} + r_{2}}

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Solution

The correct option is D $\frac{V r_{1}}{r_{1} + r_{2}}$
In steady state $C_{^{'}}^{^{'}} = 0$
$V = I [r_{1} + r_{2}]$
$V_{C} = I r_{1}$
$= \frac{V r_{1}}{r_{1} + r_{2}}$

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A metallic sphere of radius $R_{1}$ is charged to a potential V. If it is enclosed by a spherical conducting shell of radius $R_{2}$ and connected to it, its new potential will be

Q. Assertion :In a

△ A B C

, if

a < b < c

and

r

is inradius and

r_{1}, r_{2}, r_{3}

are the axradii opposite to angle

A, B, C

respectively, then

r < r_{1} < r_{2} < r_{3}

Reason:

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = \frac{r_{1} r_{2} r_{3}}{r}

\frac{R_{1}}{r_{1}} + \frac{R_{2}}{r_{2}} + \frac{R_{3}}{r_{3}} =

Q. Assertion :In a

Δ

ABC,

r_{1} + r_{2} + r_{3} - r = 4 R

Reason:

r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1} = Δ^{2}

Q. If in a

△ A B C, r_{1} r_{2} + r_{2} r_{3} + r_{3} r_{1}

is equal to
(where

r_{1}, r_{2}

and

r_{3}

are the exradii and

2 s

is the perimeter.)

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In the given circuit, the steady state voltage dropacross the capacitor C is

The correct option is D Vr1r1+r2In steady state C′′=0V=I[r1+r2]VC=Ir1 =Vr1r1+r2

In the given circuit, the steady state voltage drop
across the capacitor C is

The correct option is D $\frac{V r_{1}}{r_{1} + r_{2}}$
In steady state $C_{^{'}}^{^{'}} = 0$
$V = I [r_{1} + r_{2}]$
$V_{C} = I r_{1}$
$= \frac{V r_{1}}{r_{1} + r_{2}}$