$A$ battery of $\mathrm{emf}$ $E$ and internal resistance $r$ is connected across a resistance $R$. Resistance $R$ can be adjusted to any value greater than or equal to zero. Agraph is plotted between the current $(i)$ passing through the resistance and potential difference $(V) $ across it. Select the correct alternative $(s)$.
Medium
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The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is $31.4 \,cm$. The diameter of wire is measured as $2.4 \,cm$. The resistivity of the given wire is measured as $x \times 10^{-3} \,\Omega cm$. The value of $x$ is_______ [Take $\pi=3.14]$
In the given circuit of potentiometer, the potential difference $E$ across $AB$ ( $10\, m$ length) is larger than $E _{1}$ and $E _{2}$ as well. For key $K _{1}$ (closed), the jockey is adjusted to touch the wire at point $J_{1}$ so that there is no deflection in the galvanometer. Now the first battery $\left( E _{1}\right)$ is replaced by second battery $\left( E _{2}\right)$ for working by making $K _{1}$ open and $K _{2}$ closed. The galvanometer gives then null deflection at $J _{2}$. The value of $\frac{ E _{1}}{ E _{2}}$ is $\frac{ a }{ b },$ where $a =$ ...............
Two resistances of $400\,\Omega $ and $800\,\Omega $ are connected in series with a $6\,volt $ battery of negligible internal resistance. A voltmeter of resistance $10,000\,\Omega $ is used to measure the potential difference across $400\,\Omega $ . The error in the measurement of potential difference (in volt) approximately is
$10$ resistors, each of resistance $R$ are connected in series to a battery of $emf$ $E$ and negligible internal resistance. Then those are connected in parallel to the same battery, the current is increased $n$ times. The value of $n$ is :
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