The current in a conductor varies with time $t$ as $I=2t+3t^2$, where $I$ is in ampere and $t$ in seconds. Electric charge flowing through a section of the conductor during $t=2 \sec$ to $t=3 \sec$ is

If the ammeter in the given circuit reads $2 \mathrm{A}$, the resistance $R$ is

Figure shows a potentiometer. Length of the potentiometer wire $AB$ is $100 \mathrm{cm}$ and its resistance is $100\Omega$. EMF of the battery $E$ is $2 \mathrm{V}$. A resistance $R$ of $50\Omega$ draws current from the potentiometer. What is the voltage across $R$ when the sliding contact $C$is at the mid-point of $AB ?$

In the circuit, the galvanometer $G$ shows zero deflection. If the batteries $A$ and $B$ have negligible internal resistance, then the value of $R$ is

A circuit is shown in the figure. The e.m.f. of the battery is