The charge flowing through a conductor beginning with time $t=0$ is given by the formula $q=2t^2+3t+1\left(\mathrm{Couloms}\right)$.Find the current $i=\frac{dq}{dt}$ at the end of $5^{\mathrm{th}}$ second.

A heating coil of resistance $100 \mathrm{\Omega }$ takes $100 \mathrm{s}$ to boil certain amount of water. If a similar heating coil is connected in series with the heating coil, then the time required to boil the water is $t_{\mathrm{s}}$, while $t_{\mathrm{p}}$ time is required to boil the same amount of water if the coils are connected in parallel. What will be $\frac{t_{\mathrm{s}}}{t_{\mathrm{p}}}$?

A conducting wire of length $l$, area of cross-section $A$ and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference $V$ is developed between its ends, causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be___

The potential difference between points $A$ and $B$ of adjoining figure is

An electric cable having a resistance $R$ delivers $11 \mathrm{kW}$ of power at $220 \mathrm{V}$ to a factory. If the efficiency of transmission is $91\%$, then what is the value of $R$?

The current flowing through a wire depends on time as $I=3t^2+2t+5.$ The charge flowing through the cross section of the wire in time from $t=0$ to $t=2 \mathrm{s}$ is

Three resistors having resistances $r_1, r_2$ and ${\mathrm{r}}_3$ are connected as shown in the given circuit. The ratio $\frac{i_3}{i_1}$ of currents in terms of resistances used in the circuit is :

In a coil of resistance $100 \mathrm{\Omega }$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:

A $10 \mathrm{V}$ cell of negligible internal resistance is connected in parallel across a battery of emf $200 \mathrm{V}$ and internal resistance $38 \mathrm{\Omega }$ as shown in the figure. Find the value of current in the circuit.