If n, e, $$\tau$$ and m have their usual meanings, then the resistance of a wire of length l and cross-sectional area A is given by -

A proton and an alpha particle move in circular orbits in a uniform magnetic field. Their speeds are in the ratio of 9 : 4. The ratio of radii of their circular orbits $$\left( {{{{r_p}} \over {{r_{alpha}}}}} \right)$$ is

A coil of area 100 cm² is kept at an angle of 30$$^\circ$$ with a magnetic field of 10^$$-$$1 T. The magnetic field is reduced to zero in 10^$$-$$4 s. The induced emf in the coil is -

A 15 $$\Omega$$ resistor, an 80 mH inductor and a capacitor of capacitance C are connected in series with a 50 Hz ac source. If the source voltage and current in the circuit are in phase, then the value of capacitance is