Five current carrying conductors meet at point $$\mathrm{P}$$. What is the magnitude and direction of the current in conductor $$\mathrm{PQ}$$?

A $$10 \mathrm{~m}$$ long wire of resistance $$20 \Omega$$ is connected in series with a battery of emf $$3 \mathrm{~V}$$ (negligible internal resistance) and a resistance of $$10 \Omega$$. The potential gradient along the wire is

Only $$4 \%$$ of the total current in the circuit passes through a galvanometer. If the resistance of the galvanometer is $$G$$, then the shunt resistance connected to the galvanometer is

Two cells $$E_1$$ and $$E_2$$ having equal EMF '$$E$$' and internal resistances $$r_1$$ and $$r_2\left(r_1>r_2\right)$$ respectively are connected in series. This combination is connected to an external resistance '$$R$$'. It is observed that the potential difference across the cell $$\mathrm{E}_1$$ becomes zero. The value of '$$R$$' will be