A series $\mathrm{L}-\mathrm{C}-\mathrm{R}$ circuit containing a resistance ' $R$ ' has angular frequency ' $\omega$ '. At resonance the voltage across resistance and inductor are ' $V_R$ ' and ' $\mathrm{V}_{\mathrm{L}}$ ' respectively, then value of capacitance will be

Consider a long uniformly charged cylinder having constant volume charge density ' $\lambda$ ' and radius ' $R$ '. A Gaussian surface is in the form of a cylinder of radius ' $r$ ' such that vertical axis of both the cylinders coincide. For a point inside the cylinder $(r< R)$, electric field is directly proportional to

Two capillary tubes A and B of the same internal diameter are kept vertically in two different liquids whose densities are in the ratio $4: 3$. If the surface tensions of these two liquids are in the ratio $6: 5$, then the ratio of rise of liquid in capillary A to that in B is (assume their angles of contact are nearly equal)

For a transistor, current gain $(\beta)=50$. To change the collector current by $350 \mu \mathrm{~A}$, the base current should be changed by