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The current density is a solid cylindrical wire of radius $R ,$ as a function of radial distance $r$ is given by $J ( r )= J _{0}\left(1-\frac{ r }{ R }\right) .$ The total current in the radial region $r =0$ to $r =\frac{ R }{4}$ will be
Two resistances are connected in two gaps of a meter bridge. The balance point is $20\, cm$ from the zero end. A resistance of $15\, ohms$ is connected in series with the smaller of the two. The null point shifts to $40\, cm$. The value of the smaller resistance in $ohms$ is
Four wires $AB,\,\,BC,\,\,CD,\,\,DA$ of resistance $4\, \Omega$ each and a fifth wire $BD$ of resistance $8\, \Omega$ are joined to form a rectangle $ABCD$ of which $BD$ is a diagonal. The effective resistance between the points $A$ and $B$ is
According to Joule's law, if the potential difference across a conductor having a material of specific resistance remains constant, then the heat produced in the conductor is directly proportional to
Two wires $A$ and $B$ of the same material, having radii in the ratio $1: 2$ carry currents in the ratio $4: 1$. The ratio of drift speed of electrons in $A$ and $B$ is