Consider the circuit given here. The potential difference $V_{BC}$ between the points $B$ and $C$ is (in $V$)

The temperature coefficient of resistance of tungsten is $4.5 \times 10^{-3} \, ^{\circ}C^{-1}$ and that of germanium is $-5 \times 10^{-2} \, ^{\circ}C^{-1}$. $A$ tungsten wire of resistance $100 \, \Omega$ is connected in series with a germanium wire of resistance $R$. The value of $R$ for which the resistance of the combination does not change with temperature is .......... $\Omega$.

If the resistance of a heating coil is $484\, \Omega$ and the supply voltage is $220\, V\ AC$,how much time in $sec$ will the heater take to raise the temperature of $100\, g$ of water by $50^\circ C$?

The battery shown in the figure has an $e.m.f.$ $E$ and internal resistance $r$. The current in the circuit can be varied by sliding the contact $J$. If at any instant the current flowing through the circuit is $I$,the potential difference between the terminals of the cell is $V$,and the thermal power generated in the cell is equal to $\eta$ fraction of the total electrical power generated in it,then which of the following graphs is correct?

$A$ wire of resistance $10\, \Omega$ is bent into a circle. $P$ and $Q$ are two points on the circumference of the circle that divide the circle into a quadrant. When these two points are connected to a battery of $3\, V$ and internal resistance $1\, \Omega$, the currents passing through the two parts of the circle are:

If the cold junction is held at $0^{\circ} C$, the thermo emf $V$ of a thermocouple varies as $V = 10 \times 10^{-6} t - \frac{1}{40} \times 10^{-6} t^2$, where $t$ is the temperature of the hot junction in $^{\circ} C$. The neutral temperature and the maximum value of thermo emf are respectively: