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The resistance per centimeter of a meter bridge wire is $\mathrm{r}$, with $\mathrm{X}\ \Omega$ resistance in left gap. Balancing length from left end is at $40 \mathrm{~cm}$ with $25\ \Omega$ resistance in right gap. Now the wire is replaced by another wire of $2 \mathrm{r}$ resistance per centimeter. The new balancing length for same settings will be at
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, $h=6.63 \times 10^{-34} \,Js$ )
Twelve wires of equal length and same cross-section are connected in the form of a cube. If the resistance of each of the wires is $R$, then the effective resistance between the two diagonal ends would be
A uniform metallic wire has a resistance of $18\,\Omega $ and is bent into an equilateral triangle. Then, the resistance between any two vertices of the triangle is .................. $\Omega$
In a meter bridge experiment resistances are connected as shown in the figure. Initially resistance $P\, = 4\,\Omega $ and the neutral point $N$ is at $60\,cm$ from $A$. Now an unknown resistance $R$ is connected in series to $P$ and the new position of the neutral point is at $80\,cm$ from $A$ . The value of unknown resistance $R$ is
Two sources of equal $emf$ are connected to an external resistance $R$. The internal resistances of the two sources are ${R_1}$ and ${R_2}\,({R_2} > {R_1})$. If the potential difference across the source having internal resistance ${R_2}$ is zero, then
Three resistors of $4\,\Omega ,6\,\Omega $ and $12\,\Omega $ are connected in parallel and the combination is connected in series with a $1.5\, V$ battery of $1\,\Omega $ internal resistance. The rate of Joule heating in the $4\,\Omega $ resistor is ................ $W$