$A$ wire of $20 \Omega$ is immersed in ice. If $10 \ A$ current is passed through this wire for $1 \ minute$,the ice completely melts. The mass of the ice is nearly $(L_{\text{ice}} = 79.7 \ cal \ g^{-1})$

Two electric bulbs marked $40\,W, 220\,V$ and $60\,W, 220\,V$ are connected in series across a $220\,V$ supply,resulting in an effective power $P_1$. When they are connected in parallel across the same $220\,V$ supply,the effective power is $P_2$. The ratio $\frac{P_1}{P_2}$ is:

Two resistors with resistances $R_1$ and $R_2$ are connected in series and two capacitors with capacitances $C_1$ and $C_2$ are also connected in series. These two systems are connected to a battery of $EMF$ $\varepsilon$ as shown in the figure. The potential difference between points $a$ and $b$ is zero in the steady state if:

The cold junction of a thermocouple is maintained at $10\,^{\circ}C$. No thermo $e.m.f.$ is developed when the hot junction is maintained at $530\,^{\circ}C$. The neutral temperature is ................ $^{\circ}C$.

When $1\,g$ of hydrogen $(e.c.e. = 1.044 \times 10^{-8}\,kg/C)$ forms water,$34\,kcal$ of heat is liberated. The minimum voltage required to decompose water is ............. $V$.

$A$ wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to current,the temperature of the wire is raised by $\Delta T$ in a time $t$. $A$ number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. The value of $N$ is