In the following circuit,a bulb is rated as $1.5\, V$,$0.45\, W$. If the bulb glows with full intensity,then what will be the equivalent resistance between $X$ and $Y$? ............. $\Omega$

Two cells $A$ and $B$ of emf $2 \text{ V}$ and $1.5 \text{ V}$ respectively,are connected as shown in the figure through an external resistance $10 \text{ } \Omega$. The internal resistance of each cell is $5 \text{ } \Omega$. The potential difference $V_{A}$ and $V_{B}$ across the terminals of the cells $A$ and $B$ respectively are:

$A$ galvanometer $(G)$ of $2 \ \Omega$ resistance is connected in the given circuit. The ratio of charge in $C_1$ $(4 \ \mu F)$ and $C_2$ $(6 \ \mu F)$ is:

If the temperature of the cold junction of a thermocouple is lowered,then the neutral temperature

In the circuit shown in the figure,the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition,a current of $1 \,A$ flows through the $1 \,\Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement(s) is(are) correct?

[Given: $e^{-1}=0.36$]
$(A)$ The value of the resistance $R$ is $3 \,\Omega$.
$(B)$ The current through the $3 \,\Omega$ resistor (connected in parallel to the $1 \,\Omega$ and $R$ branches) is $2 \,A$ when $K$ is open.
$(C)$ At $t=t_0+7.2 \,\mu s$,the current in the capacitor branch is $0.6 \,A$.
$(D)$ For $t < \infty$,the charge on the capacitor is $12 \,\mu C$.

The rate of increase of thermo-e.m.f. with temperature at the neutral temperature of a thermocouple [$AIPMT$ $2011$]