In an electrical cable,there is a single wire of copper with a radius of $9 \, mm$. Its resistance is $5 \, \Omega$. The cable is replaced by $6$ different insulated copper wires,each with a radius of $3 \, mm$. Now,the total resistance of the cable will be ............... $\Omega$.

The following figures show different combinations of identical bulb$(s)$ connected to identical battery(ies). Which option is correct regarding the total power dissipated in the circuit?

The thermo emf of a hypothetical thermocouple varies with the temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts,where the ratio $a/b$ is $700^{\circ}C$. If the cold junction is kept at $0^{\circ}C$,then the neutral temperature is:

Two voltmeters $V_1$ and $V_2$ are connected in series in a $D.C.$ circuit. The reading of $V_1$ is $80 \, V$ and its sensitivity is $200 \, \Omega/V$. If the resistance of $V_2$ is $32 \, k\Omega$,what is the total voltage of the circuit in $V$?

Three wires of copper,iron,and nickel are joined to form three junctions as shown in the figure. When the temperature of junction $1$ is kept at $50\,^{\circ}\text{C}$ with the other two junctions at $0\,^{\circ}\text{C}$,the sensitive galvanometer gives a deflection of $14$ divisions. When the temperature of junction $3$ is kept at $50\,^{\circ}\text{C}$,with the other two junctions at $0\,^{\circ}\text{C}$,the galvanometer gives a deflection of $11$ divisions. Then the deflection given by the galvanometer,when the temperature of junction $2$ is kept at $50\,^{\circ}\text{C}$,with the other two junctions at $0\,^{\circ}\text{C}$,will be (in $div$)

The variation of current $(I)$ and voltage $(V)$ is as shown in figure $A$. The variation of power $P$ with current $I$ is best shown by which of the following graphs?