Physics

Inside a uniform spherical shell, electric field is zero every where & electric potential is constant but not zero, every where

Power is maximum at resonance

So, $X_L=X_C=\frac{1}{\omega C}$ ${}_{}{}_{}\frac{}{}$

$\Rightarrow C=\frac{1}{\omega *X_L}$

$=\frac{1}{250*100*{\pi }^2}$

$=4\mu F\left[{\pi }^2=10\right]$

F. B. D of Beaker

By NLM2         

$\begin{array}{l}f=ma=m{\omega }^{2}R\\ \Rightarrow m{\omega }^{2}R\le \mu N\\ R\le \mu g/{\omega }^2\end{array}$

$tan\beta =\frac{Bsin60°}{A-Bcos60°}$

$\Rightarrow \beta =ta{n}^{-1}\left(\frac{\sqrt[]{3}B}{2A-B}\right)$

$P=E{L}^2{M}^{-5}{G}^{-2}$

$=\left[M{L}^2{T}^{-2}\right]{\left[M{L}^2{T}^{-1}\right]}^2\left[M^{-5}\right]{\left[M^{-1}{L}^3{T}^{-2}\right]}^{-2}$

$=M^0{L}^0{T}^0$

$U_B=\frac{1}{2}L{l}^2............\left(i\right)$

P_R = l²R

=> 640 = (8)² R

R = $10\Omega$

from (i) 64 = $\frac{1}{2}*L*{\left(8\right)}^2$

L = 2H

$l=\frac{L}{R}=\frac{2}{10}=0.2second$        

$\frac{Q_H}{Q_L}=\frac{T_H}{T_L}$

$\Rightarrow Q_L=\frac{T_L}{T_H-T_L}*\left(Q_H-Q_L\right)$

$\Rightarrow \frac{d{Q}_L}{dt}=\frac{T_L}{T_H-T_L}.\frac{d\left(Q_H-Q_L\right)}{dt}$

$=\frac{273-10}{25-\left(-10\right)}*35$

$=263J{s}^{-1}$

$R_{eq}=0.6\Omega +\frac{\frac{4*12}{4+12}*\frac{6*8}{6+8}}{\frac{4*12}{4+12}+\frac{6*8}{6+8}}\Omega$

$=0.6\Omega +\frac{3*\frac{48}{14}}{3+\frac{48}{14}}\Omega$

$=0.6\Omega +\frac{\left(144/14\right)\Omega }{\left(\frac{90}{14}\right)}$

$\begin{array}{l}=0.6\Omega +1.6\Omega \\ =2.2\Omega \end{array}$

p = $\frac{v^2}{R_{eq}}=\frac{{\left(2.2V\right)}^2}{2.2\Omega }=2.2W$

$B_{axis}=\frac{{\mu }_{0}Nl{a}^2}{2{\left(a^2+r^2\right)}^{3/2}}$

$B_{cent}=\frac{{\mu }_{0}NI}{2a}$

Fractional change = $\frac{B_{centre}-B_{axis}}{B_{centre}}$

$=1-\frac{B_{axis}}{B_{centre}}$

$=1-\left(1-\frac{3r^2}{2a^2}\right)\left[r<<a\right]$

$=\frac{3r^2}{2a^2}$