The emf of a thermocouple,one junction of which is kept at $0\,^{\circ}C$,is given by $e = at + bt^2$. The Peltier coefficient will be

$A$ battery of internal resistance $4 \,\Omega$ is connected to the network of resistances as shown. In order to give the maximum power to the network,the value of $R$ (in $\Omega$) should be

$A$ battery with an internal resistance of $4 \Omega$ is connected to a circuit consisting of three resistors,$R$,$2R$,and $4R$,as shown in the figure. If the power generated in the circuit is maximum,then the magnitude of $R$ must be: (in $\Omega$)

In the given figure,the steady state current $I$ is ................. $A$.

$A$ wire of uniform resistance $\lambda \ \Omega/m$ is bent into a circle of radius $r$. Two radial wires, each of length $r$, are connected from the center $O$ to points $A$ and $B$ on the circumference, where the angle $\angle AOB = 90^\circ$. The equivalent resistance between points $A$ and $B$ is . . . . . . $\Omega$.

$A$ battery of emf $E$ has an internal resistance $r$. $A$ variable resistance $R$ is connected to the terminals of the battery. $A$ current $i$ is drawn from the battery. $V$ is the terminal potential difference. If $R$ alone is gradually reduced to zero,which of the following best describes $i$ and $V$?