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Two cells of emf $2\, E$ and $E$ with internal resistance $r _{1}$ and $r _{2}$ respectively are connected in series to an external resistor $R$ (see $figure$). The value of $R ,$ at which the potential difference across the terminals of the first cell becomes zero is
A copper wire of diameter $1.02\, mm$ carries a current of $1.7\, amp$. Find the drift velocity $(v_d)$ of electrons in the wire. Given $n$, number density of electrons in copper $= 8.5 \times 10^{27} /m^3$....................... $mm/sec$
In a region $10^{19}$ $\alpha -$ particels and $10^{19}$ protons per second move to the left, while $10^{19}$ electrons moves to the right per second. The current is
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
Two circuits (shown below) are called ‘Circuit $A$ ’and ‘Circuit $B$’. The equivalent resistance of ‘Circuit $a$’ is $x$ and that of ‘Circuit $B$’ is $y$ between $1$ and $2.$