The resistance of a heater coil is $110\, \Omega$. $A$ resistance $R$ is connected in parallel with it,and the combination is joined in series with a resistance of $11\, \Omega$ to a $220\, V$ main line. The heater operates with a power of $110\, W$. The value of $R$ in $\Omega$ is

The charge flowing through a resistance $R$ varies with time $t$ as $Q = at - bt^2$,where $a$ and $b$ are positive constants. The total heat produced in $R$ is

An infinite line charge of uniform electric charge density $\lambda$ lies along the axis of an electrically conducting infinite cylindrical shell of radius $R$. At time $t=0$,the space inside the cylinder is filled with a material of permittivity $\varepsilon$ and electrical conductivity $\sigma$. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density $j(t)$ at any point in the material?

What is the effective resistance between $A$ and $B$ for the given infinite resistor network?

$A$ voltmeter of resistance $998\ \Omega$ is connected to a cell of $emf$ $2\ V$ and internal resistance $2\ \Omega$. The error in the measurement of $emf$ will be:

Find the equivalent resistance across $AB$ in the given circuit.