The smallest temperature difference that can be measured with a combination of a thermocouple of thermo $e.m.f.$ $30\,\mu V$ per degree and a galvanometer of $50\,\Omega$ resistance,capable of measuring a minimum current of $3 \times 10^{-7} \, A$ is ............... $^\circ C$.

Calculate the voltage across $AB$ terminals in the given circuit.

$A$ battery of $6 \text{ V}$ is connected to the ends of a uniform wire $3 \text{ m}$ long and of resistance $100 \Omega$. The potential difference between two points $50 \text{ cm}$ apart on the wire is: (in $\text{ V}$)

$A$ $9\, V$ battery with an internal resistance of $0.5\,\Omega$ is connected across an infinite network as shown in the figure. All ammeters $A_1, A_2, A_3$ and the voltmeter $V$ are ideal. Choose the correct statement.

$A$ wire of cross-section area $A$,length $L_1$,resistivity $\rho_1$ and temperature coefficient of resistivity $\alpha_1$ is connected to a second wire of length $L_2$,resistivity $\rho_2$,temperature coefficient of resistivity $\alpha_2$ and the same area $A$,so that the wires carry the same current. The total resistance $R$ is independent of temperature for small temperature changes if (Thermal expansion effect is negligible):

Two resistors are connected in series across a battery as shown in the figure. If a voltmeter of resistance $2000 \,\Omega$ is used to measure the potential difference across the $500 \,\Omega$ resistor,the reading of the voltmeter will be ............... $V$.