A Daniel cell is balanced on $125\,cm$ length of a potentiometer wire. Now the cell is short-circuited by a resistance $2\, ohm$ and the balance is obtained at $100\,cm$. The internal resistance of the Daniel cell is .............. $ohm$
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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 copper wire of resistance $R$ is cut into ten parts of equal length. Two pieces each are joined in series and then five such combinations are joined in parallel. The new combination will have a resistance
A potentiometer wire is $100\,\, cm$ long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at $50\,\, cm$ and $10\,\, cm$ from the positive end of the wire in the two cases. The ratio of emf's is
The length of a wire of a potentiometer is $100\, cm$, and the $emf$ of its standard cell is $E\,volt$. It is employed to measure the $e.m.f$ of a battery whose internal resistance is $0.5 \,\Omega$. If the balance point is obtained at $l = 30\, cm$ from the positive end, the $e.m.f.$ of the battery is
A battery of $emf$ $10\,V$ is connected to resistances as shown in the figure. The potential difference between $A$ and $B,\,\,(V_A -V_B)$ is ................ $V$
During lighting, a current pulse, shown in figure, flows from the cloud at a height $1.5\ km$ to the ground. If the breakdown electric field of humid air is about $400\ kVm^{-1}$ , the energy released during lighting would be (in unit of $10^9\ J$ )