In an electric circuit, a cell of certain emf provides a potential difference of \(1.25\, {V}\) across a load resistance of \(5\, \Omega .\) However, it provides a potential difference of \(1\, {V}\) across a load resistance of \(2\, \Omega\). The \(emf\) of the cell is given by \(\frac{x}{10} v\). Then the value of \(x\) is ..... .

A conductor lies along the \(z-\)axis \(a\) \(-1.5\)\( \le Z < 1.5\,m\) carries a fixed current of \(10.0\ A\) in \( - {\hat a_z}\) direction (see figure). For a field \(\vec B\) \(=\) \(3.0 \times  10^{-4}\)  \(e^{-0.2x}\) \({\hat a_y}\,T\) find the power required to move the conductor at constant speed to \(x = 2.0\ m, y = 0\ m\) in \(5 \times 10^{-3}\ s\). Assume parallel motion along the \(x-\)axis........\( W\)

The electric potential as a function of \(x, y\) is given by \(V = 5(x^2 - y^2)\) V. The electric field at a point \((2, 3)\) m is __________ V/m.

A wire \(X\) of length \(50\; cm\) carrying a current of \(2\,A\) is placed parallel to a long wire \(Y\) of length \(5\,m\). The wire \(Y\) carries a current of \(3\,A\). The distance between two wires is \(5\,cm\) and currents flow in the same direction. The force acting on the wire \(Y\) is.

A circular coil having \(N\,turns\) and radius \(r\) carries a current. It is held in the \(XZ\) plane in a magnetic field \(B\hat i\) . The torque on the coil due to the magnetic field is

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is \(40\,cm.\) The area of the image is \(9\,times\) that of the square. The focal length of the lens is........\(cm\)

A cylindrical block of wood (density \(= 650\, kg\, m^{-3}\)), of base area \(30\,cm^2\) and height \(54\, cm\), floats in a liquid of density \(900\, kg\, m^{-3}\) . The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length ..... \(cm\) (nearly)

A very long wire \(ABDMNDC\) is shown in figure carrying current \(I. AB\) and \(BC\) parts are straight, long and at right angle. At \(D\) wire forms a circular turn \(DMND\) of radius \(R. AB.\) \(\mathrm{BC}\) parts are tangential to circular turn at \(\mathrm{N}\) and \(D\). Magnetic field at the centre of circle is

\(ABC\) is a plane lamina of the shape of an equilateral triagnle. \(D,\) \(E\) are mid points of \(AB\), \(AC\) and \(G\) is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through \(G\) and perpendicular to the plane \(ABC\) is \(I _{0} .\) If part \(ADE\) is removed, the moment of inertia of the remaining part about the same axis is \(\frac{ NI _{0}}{16}\) where \(N\) is an integer. Value of \(N\) is