The current in a wire varies with time according to relation $I = 4 + 2t$. The quantity of charge which has passed through a crosssectionn of the wire during the time $t = 2\, s$ to $t = 6\, s$ will be .............. $\mathrm{C}$
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Under what condition current passing through the resistance $R$ can be increased by short circuiting the battery of emf $E_2$. The internal resistances of the two batteries are $r_1$ and $r_2$ respectively.
In the network shown in the figure, each of the resistance is equal to $2\,\Omega $. The resistance between the points $A$ and $B$ is .............. $\Omega$
A wire of $1 \,\Omega$ has a length of $1\, m$. It is stetched till its length increases by $25\, \%$. The percentage change in resistance to the neartest integer is .....$\%$
A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V _0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio $P_2: P_1$ is $\sqrt{x}: 1$. The value of $x$ is $.............$.
An electrical power line, having a total resistance of $2 \Omega$, delivers $1 \,kW$ at $220\, V$. The efficiency of the transmission line is approximately $.......\%$
A cell can be balanced against $110\,\, cm$ and $100\,\, cm$ of potentiometer wire, respectively with and without being short circuited through a resistance of $10 \,\,\Omega$. Its internal resistance is ............... $\Omega$