A capacitor is discharging through a resistor R. Consider in time t1, the energy stored in the capacitor reduces to half of its initial value and in time t2, the charge stored reduces to one eighth of its initial value. The ratio t2t1 will be
Held on 29 Jun 2022 · Verified 6 Jul 2026.
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A short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 Gauss, experiences a torque of $0.016 \mathrm{~N}. \mathrm{m}$. The work done in moving it from most stable to most unstable position is $\alpha \times 10^{-3} \mathrm{~J}$. The value of $\alpha$ is $\_\_\_\_$.
A small cube of side $1$ mm is placed at the centre of a circular loop of radius $10$ cm carrying a current of $2$ A. The magnetic energy stored inside the cube is $\alpha \times 10^{-14}$ J. The value of $\alpha$ is _______. ($\mu_o = 4\pi \times 10^{-7}$ Tm/A, $\pi = 3.14$)
A circular coil of radius $2$ cm and $125$ turns carries a current of $1$ A. The coil is placed in a uniform magnetic field of magnitude $0.4$ T. The axis of the coil makes an angle of $30°$ with the direction of the magnetic field. The torque acting on the coil is $\alpha \times 10^{-4}$ N.m. The value of $\alpha$ is ______. ($\pi=3.14$)
$1\,\mu$C charge moving with velocity $\vec{v} = \left(\hat{i} - 2\hat{j} + 3\hat{k}\right)$ m/s in the region of magnetic field $\vec{B} = \left(2\hat{i} + 3\hat{j} - 5\hat{k}\right)$ T. The magnitude of force acting on it is $\sqrt{\alpha} \times 10^{-6}$ N. The value of $\alpha$ is _______.
A series LCR circuit with $R = 20\ \Omega$, $L = 1.6\text{ H}$ and $C = 40\ \mu\text{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ $\Omega$.
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