An experiment is performed to determine the \(I-V\) characteristics of a Zener diode, which has a protective resistance of \(R = 100 \,\Omega ,\) and a maximum power of dissipation rating of \(1\,W\) .The minimum voltage range of the \(DC\) source in the circuit is

A particle of mass \(2\, kg\) is moving such that at time \(t\), its position, in meter, is given by \(\overrightarrow r \left( t \right) = 5\hat i - 2{t^2}\hat j\) . The angular momentum of the particle at \(t\, = 2\, s\) about the origin in \(kg\, m^{-2}\, s^{-1}\) is

A charge \(Q\) is moving \(\overrightarrow{dl}\) distance in the magnetic field \(\overrightarrow{ B }\). Find the value of work done by \(\overrightarrow{ B }\).

A thermally insulted vessel contains \(150\, g\) of water at \(0\,^oC\). Then the air from the vessel is pumped out a adiabatically. A fraction of water turns into ice and the rest evaporates at \(0\,^oC\) itself. The mass of evaporated water will be closes to ....... \(g\) (Latent heat of vaporization of water \(= 2.10 \times10^6\, Jkg^{-1}\) and Laten heat of Fusion of water \( = 3.36 \times10^5\,Jkg^{-1}\) )

A parallel plate capacitor of capacitance \(12.5 \mathrm{pF}\) is charged by a battery connected between its plates to potential difference of \(12.0 \mathrm{~V}\). The battery is now disconnected and a dielectric slab \(\left(\epsilon_{\mathrm{r}}=6\right)\) is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _______.\(\times 10^{-12} \mathrm{~J}\).

Three masses \(m_1 = 4\) kg, \(m_2 = 4\) kg and \(m_3 = 6\) kg are suspended from a fixed smooth frictionless pulley as shown in the figure below. The value of \(T_1/T_2\) is _____.
(take \(g = 10\) m/s\(^2\))

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension \(70 \mathrm{dyn} / \mathrm{cm}\) and glass water contact angle \(\simeq 0^{\circ}\)) with \(30^{\circ}\) inclined with vertical. The length of water risen in the capillary is ________ cm.
\(\left(\right.\) Take \(\left.\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right)\)

A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is \(91.6 \%\), then the loss of power in units of \(\mathrm{cal} / \mathrm{s}\) is _________.

The resistance per centimeter of a meter bridge wire is \(\mathrm{r}\), with \(\mathrm{X}\  \Omega\) resistance in left gap. Balancing length from left end is at \(40 \mathrm{~cm}\) with \(25\  \Omega\) resistance in right gap. Now the wire is replaced by another wire of \(2 \mathrm{r}\) resistance per centimeter. The new balancing length for same settings will be at _______.

The velocity (\(v\)) versus time (\(t\)) plot of a particle is shown in the figure, for a time interval of \(40\text{ s}\). The total distance travelled by the particle and the average velocity during this period are, respectively _______.