In a series LR circuit, power of 400W is dissipated from a source of 250 V, 50 Hz. The power factor of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as $$\left( {{n \over {3\pi }}} \right)$$ $$\mu $$F, then value of n is __________.

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1 + $$\beta $$)v, this angle changes to 45^o. The value of $$\beta $$ is close to :

When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by
y(t) = y₀ sin² $$\omega $$t, where 'y' is measured from the lower end of unstretched spring. Then $$\omega $$ is:

A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit :