$A$ 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 $n\,?$

In the given circuit, the internal resistance of the battery is $0.50\, \Omega$. What is the charge on the plates of the $5\, \mu F$ capacitor in $\mu C$?

The temperature of the cold junction of a thermocouple is $0\,^{\circ}C$ and the temperature of the hot junction is $T\,^{\circ}C$. The e.m.f. is $E = 16T - 0.04T^2 \, \mu\text{V}$. The temperature of inversion is ................ $^{\circ}C$.

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:

Given below are two statements:
Statement $I$: $A$ uniform wire of resistance $80\,\Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5\,\Omega$.
Statement $II$: Two resistances $2\,R$ and $3\,R$ are connected in parallel in an electric circuit. The value of thermal energy developed in $3\,R$ and $2\,R$ will be in the ratio $3:2$.
In the light of the above statements,choose the most appropriate answer from the options given below.

The charge flowing through a resistance $R$ varies with time as $Q = 2t - 8t^2$. The total heat produced in the resistance is (for $0 \leq t \leq \frac{1}{8} \ s$)