Physics

$\mathrm{B}=\frac{\mathrm{E}}{\mathrm{C}}=\frac{48}{3*{10}^8}=16*{10}^{-8}$

$=1.6*{10}^{-7}\mathrm{T}$

Capacitive reactance $=\frac{1}{\omega \mathrm{C}}={\mathrm{X}}_{\mathrm{c}}$ (say) on decreasing the operating frequency $\omega$  reduces

As $X_c$ is inversely proportional to $\omega$ the value of $X_c$  increase

$\therefore {\mathrm{I}}_{\mathrm{C}}={\mathrm{I}}_{\mathrm{D}}$

$=\frac{{\mathrm{V}}_{\mathrm{o}}}{{\mathrm{X}}_{\mathrm{c}}}$

As ${\mathrm{X}}_{\mathrm{c}}$  increases, therefore displacement current Id decreases.

For transformer

$\left(\frac{i_p}{i_s}\right)=\left(\frac{V_s}{V_P}\right)=\left(\frac{N_s}{N_P}\right)$

For bulb, $\mathrm{V}\mathrm{s}=12\mathrm{V}$

$\begin{array}{rr}& {\mathrm{i}}_{\mathrm{s}}=\left(\frac{60}{12}\right)=5\mathrm{A}\\ & \Rightarrow \frac{{\mathrm{i}}_{\mathrm{p}}}{5}=\left(\frac{12}{220}\right)\\ & \mathrm{}{\mathrm{i}}_{\mathrm{P}}=\frac{60}{220}=\left(\frac{3}{11}\right)=0.27\mathrm{A}\end{array}$

Yes. Angular Velocity is a vector quantity i.e. it has directions. The direction of rotation can influence the sign of angular velocity's value. If the movement of the object is anticlockwise, the sign will be positive. Similarly, if the movement of the object is clockwise, the sign will be negative.

For resonance frequency

$\begin{array}{rr}& \omega \mathrm{L}=\frac{1}{\omega \mathrm{C}}\\ & \Rightarrow \omega =\frac{1}{\sqrt[]{\mathrm{L}\mathrm{C}}}=\frac{1}{\sqrt[]{10*{10}^{-3}*1*{10}^{-6}}}\\ & =\frac{1}{\sqrt[]{{10}^{-8}}}={10}^4\mathrm{r}\mathrm{a}\mathrm{d}/\mathrm{s}\mathrm{e}\mathrm{c}\\ & \mathrm{f}=\left(\frac{\omega }{2\pi }\right)=\frac{{10}^4}{2\pi }=1.59\mathrm{k}\mathrm{H}\mathrm{z}\end{array}$

Magnetic energy stored in an inductor $=\frac{1}{2}{\mathrm{L}\mathrm{I}}^2$

$\begin{array}{rr}& =\frac{1}{2}*4*{10}^{-6}*(2{)}^2\\ & =8\mu \mathrm{J}\end{array}$

${\text{?}\mathrm{}}_{\mathrm{s}}\stackrel{?}{\mathrm{B}}\cdot \mathrm{d}\stackrel{?}{\mathrm{A}}=0\mathrm{}$ (No monopole exist)

Even if the torque is same, the rotation of a body can be slow or fast depending on the distribution of mass along the surface area. If the mass of a body is more on the axis area, it's speed of rotation will be faster as compared to the body whose mass is accumulated away from the axis due to which the body will resist the angular acceleration.

For conductors α $\alpha$  is (+ve)

For semiconductors $\alpha$  is (-ve)