The maximum power delivered to resistance $R$ is ............... $W$.

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 thermo emf of a thermocouple is given by $E = aT + bT^2$,where $\frac{a}{b} = -200^{\circ}C$. If the cold junction is kept at $30^{\circ}C$,then the inversion temperature is ($\varepsilon$ in volt,$T$ in centigrade). (in $K$)

$A$ battery consists of a variable number $n$ of identical cells (each having electromotive force $\varepsilon$ and internal resistance $r$) which are connected in series. The terminals of the battery are short-circuited and the current $I$ is measured. Which of the graphs shows the correct relationship between $I$ and $n\,?$

Two electric bulbs marked $25\ W - 220\ V$ and $100\ W - 220\ V$ are connected in series to a $440\ V$ supply. Which of the bulbs will fuse?

$A$ 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