In potentiometer experiment, the balancing length is $$8 \mathrm{~m}$$ when two cells $$E_1$$ and $$E_2$$ are joined in series. When two cells are connected in opposition the balancing length is $$4 \mathrm{~m}$$. The ratio of the e.m.f. of the two cells $$\left(\frac{E_1}{E_2}\right)$$ is

A wire of length $$3 \mathrm{~m}$$ connected in the left gap of a meter-bridge balances $$8 \Omega$$ resistance in the right gap at a point, which divides the bridge wire in the ratio $$3: 2$$. The length of the wire corresponding to resistance of $$1 \Omega$$ is

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