Tag: physics

frequency increased by $20\%
$$\Rightarrow f^{'}=\dfrac{6}{5}f$
$\therefore \sqrt{T^{'}}=\dfrac{6}{5}\sqrt{T}$
$\sqrt{T^{'}}=\sqrt{\dfrac{144}{100}}T$
$\therefore$ Tension is to be increased by $44\%$

$f\propto \dfrac{1}{l}\sqrt{\dfrac{T}{\mu}}$
$\Rightarrow l\propto \sqrt{T}$
$\therefore \dfrac{l _{1}}{l _{2}}=\sqrt{\dfrac{T _{1}}{T _{2}}}=\sqrt{\dfrac{8}{7}}$
$\dfrac{1}{\sqrt{7}l _{2}}=\dfrac{\sqrt{8}}{\sqrt{7}}$
$\Rightarrow l _{2}=\dfrac{1}{\sqrt{8}}$

Permittivity of metals is very high comparable to the permittivity of free space. So dielectric constant for metal is infinite.

Displacement current, ${i _d} = {\varepsilon _ \circ }A\frac{{dE}}{{dt}}$
where, $A$ is area and $E$ is electric field
$\begin{array}{l}E = \frac{e}{d} = \frac{{4\sin (100\pi t)}}{d}\{i _d} = {\varepsilon _ \circ }A \times \frac{1}{d}\left[ {\frac{d}{{dt}}\left( {4\sin 100\pi t} \right)} \right]\ = \frac{{{\varepsilon _ \circ }A}}{d}.4(cos100\pi t) \times 100\pi \ = C.400\pi .cos100\pi t\{\left( {{i _d}} \right) _{\max }} = \left( {10 \times {{10}^{ - 6}}} \right) \times 400\pi A\ = 4\pi  \times {10^{ - 3}}A = 4\pi mA\end{array}$

The dielectric is a material through which no electric current passes. Here the given materials-plastic, mica and porcelain are all the  dielectric because current can not pass through them.

Ammonia and $HCl$ are polar molecules since they have a net dipole moment towards a particular direction. Both water and benzene are non-polar molecules. But water is a conductor of electricity, whereas benzene is a dielectric (insulator).

Breakdown voltage for a dielectric is the maximum voltage at which, applied electric field becomes so high that electrons break up from the molecules of dielectric and becomes free inside the dielectric due to this dielectric becomes conductive. 

The capacitance of a parallel plate capacitor filled with the given material of dielectric constant $\kappa$ is given by:

The value of dielectric constant for air at room temperature $ (25^{o}C , or 77^{o}F )$ is $1.00059$ .