In an experiment to determine the velocity of sound in air at room temperature using a resonance tube, the first resonance is observed when the air column has a length of 20.0 cm for a tuning fork of frequency 400 Hz is used. The velocity of the sound at room temperature is 336 ms^$$-$$1. The third resonance is observed when the air column has a length of _____________ cm.

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance 2000 $$\Omega$$ is used to measure the potential difference across 500 $$\Omega$$ resistor, the reading of the voltmeter will be ___________ V.

A potential barrier of 0.4 V exists across a p-n junction. An electron enters the junction from the n-side with a speed of 6.0 $$\times$$ 10⁵ ms^$$-$$1. The speed with which electron enters the p side will be $${x \over 3} \times {10^5}$$ ms^$$-$$1 the value of x is _____________.

(Given mass of electron = 9 $$\times$$ 10^$$-$$31 kg, charge on electron = 1.6 $$\times$$ 10^$$-$$19 C.)

The displacement current of 4.425 $$\mu$$A is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of 10⁶ Vs^$$-$$1. The area of each plate of the capacitor is 40 cm². The distance between each plate of the capacitor is x $$\times$$ 10^$$-$$3 m. The value of x is __________.

(Permittivity of free space, E₀ = 8.85 $$\times$$ 10^$$-$$12 C² N^$$-$$1 m^$$-$$2).