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# Tag Archives: ratio

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## A Question from Current Electricity

Pratham asked:

The resistances of 2 bulbs are in the ratio 1:2.if they are joined in series,find the ratio of the energy consumed by the 2 bulbs?

Answer:

When connected in series, the same current flows through each of the resistors. Therefore, the energy dissipated is directly proportional to their resistances. That is, the ratio of energy dissipated will nbe same as the ratio of resistances. (1:2)

## de Broglie Wavelength

Alpha particle and a proton are accelerated from rest by the same potential. Find the ratio of their de- broglie wavelength

(Asked by Amritha)

Answer:

Charge of alpha particle = 2e

Mass of alpha particle = 4 u

Charge of proton = e

mass of proton = u

The energy acquired by proton when accelerated through a pd of V,

E=eV

The momentum acquired by proton=${\sqrt{2ueV}}$

The de Broglie wavelength is given by $\lambda =\frac{h}{mv}$

Therefore, de Broglie wavelength of Proton, $\lambda _{proton}=\frac{h}{\sqrt{2ueV}}$

Similarly,$\lambda _{alpha}=\frac{h}{\sqrt{2\times 4u\times 2e\times V}}$

$\frac{\lambda _{alpha}}{\lambda _{proton}}=\frac{\sqrt{2ueV}}{\sqrt{2\times 4u\times 2e\times V}}=\frac{1}{2\sqrt{2}}$

## A numerical problem on Drift velocity

Two conducting wires X and Y of same diameter but different materials are joined in series across a battery . if the number density of electrons in X is twice that in Y . Find the ratio of drift velocity of electrons in the two wires.
(Adithya Singh asked this)

## Power factor in AC circuits

Dany Asked:

“what is meant by power factor?”

Ans:

In AC circuits, Power factor is defined as the ratio of true power to apparent power.

$Power Factor =\frac{True Power}{Apparent Power}$

If φ is the phase difference between E and I, then

True Power = EvIv cos φ and the Apparent Power is EvIv

Therefore,

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