Due to cold weather a 1m water pipe of cross-sectional area 1 cm² is filled with ice at -10°C. Resistivity heating is used to melt the ice. Current of 0.5A is passed through 4 k $\Omega$  resistance. Assuming that all the heat produced is used for melting, what is the minimum time required?

(Given latent heat of fusion for water/ice = 3.33 * 10⁵ J kg^-1, specific heat of ice = 2 * 10³ J kg^-1 and density of ice = 10³ kg/m³)

A wire of length 'l' and resistance $100\Omega$  is divided into 10 equal parts. The first 5 parts are connected in series while the next 5 parts are connected in parallel. The two combinations are again connected in series. The resistance of this final combination is:

A thin spherical shell is charged by some source. The potential difference between the two points $C$ and $P$  (in V) shown in the figure is:

(Take  $\frac{1}{4\pi {\epsilon }_0}=9\times 10^9$  SI units)

A uniform heating wire of resistance 36 $\Omega$  is connected across a potential difference of 240V. The wire is then cut into half and a potential difference of 240 V is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be 1 : x, where x is________.

The terminal voltage of the battery, whose emf is 10 V and internal resistance $1\Omega$ , when connected through an external resistance of $4\Omega$  as shown in the figure is:

A current of 5A is passing through a non-linear magnesium wire of cross – section 0.04m². At every point the direction of current density is at an angle of 60° ;with unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: (Resistivity of magnesium $\rho =44\times 10^{-8}\Omega m)$ <!-- [if gte mso 9]><xml> </xml><![endif]-->