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

The Peltier coefficient is $2 \times 10^{-9} \, V$. How much heat in $ergs$ is produced when a current of $2.5 \, A$ is passed for $2 \, minutes$?

$A$ cell of emf $E$ is connected to a resistance $R_{1}$ for time $t$ and the amount of heat generated in it is $H$. If the resistance $R_{1}$ is replaced by another resistance $R_{2}$ and is connected to the cell for the same time $t$, the amount of heat generated in $R_{2}$ is $4H$. Then the internal resistance $r$ of the cell is:

Three $60\, W$ light bulbs are mistakenly wired in series and connected to a $120\, V$ power supply. Assume the light bulbs are rated for single connection to $120\, V$. With the mistaken connection,the power dissipated by each bulb is: .................. $W$

$A$ room has an $AC$ running for $5$ hours a day at a voltage of $220$ $V$. The wiring of the room consists of $Cu$ wire of $1$ $mm$ radius and a length of $10$ $m$. Power consumption per day is $10$ commercial units. What fraction of it goes into Joule heating in the wires? What would happen if the wiring is made of aluminium of the same dimensions? $(\rho_{Cu} = 1.7 \times 10^{-8} \, \Omega m, \rho_{Al} = 2.7 \times 10^{-8} \, \Omega m)$

The thermo emf of a hypothetical thermocouple varies with the temperature $\theta$ of the hot junction as $E = a\theta + b\theta^2$ in volts,where the ratio $a/b$ is $700^{\circ}C$. If the cold junction is kept at $0^{\circ}C$,then the neutral temperature is: