In the circuit shown in Fig. , the heat produced in $5\mathrm{\Omega }$ resistor, due to the current flowing through it is $10$ calorie per second. Find the heat produced in $4\mathrm{\Omega }$ resistor.

A heater is designed to operate with a power of $1000 \mathrm{W}$ in a $100 \mathrm{V}$ line. It is connected in combination with a resistance of $10\mathrm{\Omega }$ and a resistance $\mathrm{R}$ to a $100 \mathrm{V}$ mains, as shown in Fig. . What should be the value of $\mathrm{R}$ so that the heater operates with a power of $62.5 \mathrm{W}$ ?

Three equal resistors, each of $\mathrm{R}$ ohm, are connected as shown in Fig. . A battery of $2$ volt and of internal resistance $0.1 \mathrm{ohm}$ is connected across the circuit. Calculate the value of $\mathrm{R}$ for which the heat generated in the circuit is maximum.

Determine the currents through the resistors ${\mathrm{R}}_1, {\mathrm{R}}_2$ and ${\mathrm{R}}_3$ shown in Fig.

Find the $emf\left({\mathcal{\epsilon }}_0\right)$ and internal resistance $\left(r_0\right)$ of a battery which is equivalent to a parallel combination of two batteries of emfs ${\mathrm{\epsilon }}_1$ and ${\epsilon }_2$ and internal resistances ${\mathrm{r}}_1$ and $r_2$ respectively, with polarities as shown in Fig.

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$\text{'} \mathrm{n}\text{'}$ cells, each of emf $\text{'}\mathrm{e}\text{'}$ and internal resistance $\text{'}\mathrm{r}\text{'}$ are connected in a closed circuit so that the positive terminal of a cell is joined to the negative terminal of the next, as shown in Fig. . Any two points of the circuit are connected by an external resistance $\mathrm{R}$. Find the current in $\mathrm{R}.$

Find the current flowing through the resistance ${\mathrm{R}}_1$ of the circuit shown in Fig. . Given ${\mathrm{R}}_1=10 \mathrm{\Omega }, {\mathrm{R}}_2=20 \mathrm{\Omega }$ and ${\mathrm{R}}_3=30\mathrm{\Omega }$ and the potentials of points 1,2 and 3 are ${\mathrm{V}}_1=10\mathrm{V}, {\mathrm{V}}_2=6 \mathrm{V}$ and ${\mathrm{V}}_3=5 \mathrm{V}$.

Problem 40. A part of the circuit in a steady state along with the currents flowing in the branches, the values of resistance, etc. is shown in Fig.  Calculate the energy stored in the capacitor.

In the circuit shown in Fig. , find the current through the $4\mathrm{\Omega }$ resistor.