In the circuit shown in the figure,the $5\,\Omega$ resistance develops $20.00\,cal/s$ due to the current flowing through it. The heat developed in the $2\,\Omega$ resistance (in $cal/s$) is

Consider a block of conducting material of resistivity $\rho$ shown in the figure. Current $I$ enters at $A$ and leaves from $D$. We apply the superposition principle to find the voltage $\Delta V$ developed between $B$ and $C$. The calculation is done in the following steps: $(i)$ Take current $I$ entering from $A$ and assume it to spread over a hemispherical surface in the block. $(ii)$ Calculate the field $E(r)$ at distance $r$ from $A$ by using Ohm's law $E=\rho j$,where $j$ is the current per unit area at $r$. $(iii)$ From the $r$ dependence of $E(r)$,obtain the potential $V(r)$ at $r$. $(iv)$ Repeat $(i), (ii)$ and $(iii)$ for current $I$ leaving $D$ and superpose results for $A$ and $D$. $\Delta V$ measured between $B$ and $C$ is

Two current elements $P$ and $Q$ have current-voltage characteristics as shown below. Which of the graphs given below best represents the current-voltage characteristics when $P$ and $Q$ are in series?

Two wires '$A$' and '$B$' of the same material have their lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. The two wires are connected in parallel across a battery. The ratio of the heat produced in '$A$' to the heat produced in '$B$' for the same time is

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 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 $K$)