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A cell having an emf $\varepsilon$ and internal resistance $r$ is connected across a variable external resistance $R.$ As the resistance $R$ is increased, the plot of potential difference $V$ across $R$ is given by
When a wire of uniform cross-section $a$, length $l$ and resistance $R$ is bent into a complete circle, resistance between any two of diametrically opposite points will be
In the given circuit ' $a$ ' is an arbitrary constant. The value of $m$ for which the equivalent circuit resistance is minimum, will be $\sqrt{\frac{ x }{2}}$. The value of $x$ is ...........