The resistance per centimeter of a meter bridge wire is $$r$$, with $$X \Omega$$ resistance in left gap. Balancing length from left end is at $$40 \mathrm{~cm}$$ with $$25 \Omega$$ resistance in right gap. Now the wire is replaced by another wire of $$2 r$$ resistance per centimeter. The new balancing length for same settings will be at

Two conductors have the same resistances at $$0^{\circ} \mathrm{C}$$ but their temperature coefficients of resistance are $$\alpha_1$$ and $$\alpha_2$$. The respective temperature coefficients for their series and parallel combinations are :

When a potential difference $$V$$ is applied across a wire of resistance $$R$$, it dissipates energy at a rate $$W$$. If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:

A potential divider circuit is shown in figure. The output voltage V$$_0$$ is :