What is the maximum number of $50 \, W - 100 \, V$ bulbs that can be connected in parallel to a battery of $120 \, V$ and $10 \, \Omega$ internal resistance so that they glow with maximum intensity?

$A$ wire of uniform resistance $\lambda \ \Omega/m$ is bent into a circle of radius $r$. Two radial wires, each of length $r$, are connected from the center $O$ to points $A$ and $B$ on the circumference, where the angle $\angle AOB = 90^\circ$. The equivalent resistance between points $A$ and $B$ is . . . . . . $\Omega$.

Two wires of resistances $R_1$ and $R_2$ have temperature coefficients of resistance $\alpha_1$ and $\alpha_2$ respectively. If these are joined in series,the effective temperature coefficient of resistance is:

The figure shows three similar lamps $L_1, L_2$,and $L_3$ connected across a power supply. If the lamp $L_3$ fuses,how will the brightness emitted by $L_1$ and $L_2$ change?

Find the potential difference between points $A$ and $B$ in the following circuit. (in $V$)

$A$ battery with an internal resistance of $4\,\Omega$ is connected to a circuit as shown in the figure. For the circuit to receive maximum power,the value of $R$ should be ..... $\Omega$.