In the circuit shown in the figure, the heat produced in the $5\, \Omega$ resistance is $10\, \text{cal/sec}$. The heat produced in the $4\, \Omega$ resistance is ................ $\text{cal/sec}$.

Two cells of $e.m.f.$ $E_1$ and $E_2$ and of negligible internal resistances are connected with two variable resistors as shown in the figure. When the galvanometer shows no deflection,the values of the resistances are $P$ and $Q$. What is the value of the ratio $E_2/E_1$?

The three resistances $A, B$ and $C$ have values $3R, 6R$ and $R$ respectively. When some potential difference is applied across the network,the thermal powers dissipated by $A, B$ and $C$ are in the ratio

In the given circuit, the cells have zero internal resistance. The currents (in Amperes) passing through resistance $R_1$ and $R_2$ respectively, are

In the given circuit,the potential difference between points $P$ and $Q$ is . . . . . . (in $\text{ V}$)

The series combination of two batteries,both of the same emf $10 \; V,$ but different internal resistances of $20 \; \Omega$ and $5 \; \Omega,$ is connected to the parallel combination of two resistors $30 \; \Omega$ and $R \; \Omega.$ If the voltage difference across the battery of internal resistance $20 \; \Omega$ is zero,the value of $R$ (in $\Omega$) is: