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A wire of length $5\,m$ and radius $1\,mm$ has a resistance of $1\, ohm$. What length of the wire of the same material at the same temperature and of radius $2\,mm$ will also have a resistance of $1\, ohm$ .............. $m$
Consider a metallic cube of edge length $L$. Its resistance, $R$, measured across its opposite faces is $R =\frac{ m _{ e } v }{ ne ^2 L ^2}$, where $n$ is the number density and $v$ is the drift speed of electrons in the cube, and $e$ and $m _{ e }$ are the charge and mass of an electron respectively. Assuming the de-Broglie wavelength of the electron to be $L$, the maximum resistance of the sample is closest to ............. $\,\Omega$ $\left(e=1.60 \times 10^{-19} \,C ; m _{ e }=9.11 \times 10^{-31} \,kg\right.$; Planck's constant, $h=6.63 \times 10^{-34} \,Js$ )
A cell of internal resistance $1.5\,\Omega $ and of $e.m.f.$ $1.5\, volt$ balances $500\, cm$ on a potentiometer wire. If a wire of $15\,\Omega $ is connected between the balance point and the cell, then the balance point will shift
An electric current flows along an insulated strip $PQ$ of a metallic conductor. The current density in the strip varies as shown in graph of figure. Which one of the following statements could explain this variation ?
In an aluminium $(A1)$ bar of square cross section, a square hole is drilled and is filled with iron ( $Fe$ ) as shown in the figure. The electrical resistivities of $A 1$ and $Fe$ are $2.7 \times 10^{-8} \ \Omega m$ and $1.0 \times 10^{-7} \ \Omega m$, respectively. The electrical resistance between the two faces $P$ and $Q$ of the composite bar is