Five current carrying conductors meet at a point '$$\mathrm{O}$$' as shown in figure. The magnitude and direction of the current in conductor '$$O P$$' is

An alternating voltage of frequency '$$\omega$$' is induced in electric circuit consisting of an inductance '$$L$$' and capacitance '$$C$$', connected in parallel. Then across the inductance coil

A gas is compressed at a constant pressure of $$50 \mathrm{~N} / \mathrm{m}^2$$ from a volume of $$10 \mathrm{~m}^3$$ to a volume of $$4 \mathrm{~m}^3$$. Energy of $$100 \mathrm{~J}$$ is then added to the gas by heating. Its internal energy is

The reactance of capacitor at $$50 \mathrm{~Hz}$$ is $$5 \Omega$$. If the frequency is increased to $$100 \mathrm{~Hz}$$, the new reactance is