If a high power heater is connected to electric mains,then the bulbs in the house become dim,because there is a

$A$ wire of resistance $R$ is bent in the form of a circular loop. Two points on the circle separated by a quarter circumference are connected to a battery of emf $E$ and negligible internal resistance. The heat generated in the wire per second is

In the given circuit,the internal resistance of the $18\,V$ cell is negligible. If $R_1 = 400\,\Omega$,$R_3 = 100\,\Omega$,and $R_4 = 500\,\Omega$,and the reading of an ideal voltmeter across $R_4$ is $5\,V$,then the value of $R_2$ will be ........... $\Omega$.

If each resistance in the figure is $9 \Omega$,then the reading of the ammeter $(A)$ is (in $A$)

Current $I$ is flowing through two materials having electrical conductivities $\sigma_1$ and $\sigma_2$ respectively $(\sigma_1 > \sigma_2)$ as shown in the figure. The total amount of charge at the junction of the materials is

In the circuit shown in the figure,no current flows through the ideal ammeter. If the internal resistance of the cell is negligible,the value of unknown resistance $R$ is .............. $\Omega$.