Answer the questions.[Phy-2M]

Question 12 Marks

Several electric bulbs designed to be used on a 220 V electric supply line are rated 10 W . How many lamps can be connected in parallel with each other across the two wires of 220 V line if the maximum allowable current is 5 A ?

Answer

Let current through each bulb be I.
P = VI, 10 = 220 I
$\mathrm{I}=\frac{1}{22} \mathrm{~A}$
Let n such bulbs be connected in series.
Current through n bulbs $=5 \mathrm{~A}$
$n$ (current in 1 bult) = 5
$\mathrm{n} \frac{1}{22}=5$
$\mathrm{n}=110$
110 such bulbs can be lighted within allowable limit of 5 A .

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Question 22 Marks

A copper wire has diameter 0.5 mm and resistivity $1.6 \times 10^{-8} \Omega \mathrm{~m}$. What will be the length of this wire to make its resistance $10 \Omega$ ? How much does the resistance change if the diameter is doubled?

Answer

$\mathrm{d}=0.5 \mathrm{~mm}=0.5 \times 10^{-3} \mathrm{~m}=5 \times 10^{-4} \mathrm{~m} ; \rho=1.6 \times 10^{-8 \Omega} \mathrm{~m}, \mathrm{l}=? ; \mathrm{R}=10 \Omega$
$l=\frac{R \pi \mathrm{~d}^{2}}{4 \rho}=\frac{10}{4} \times \frac{22}{7} \times \frac{\left(5 \times 10^{-4}\right)^{2}}{1.6 \times 10^{-8}}$
$\begin{aligned} & R=\frac{\rho l}{A}=\frac{\rho l}{\frac{\pi \mathrm{~d}^2}{4}}=\frac{4 \rho l}{\pi \mathrm{~d}^2} \\ & l=\frac{220}{28} \times \frac{25}{1.6}=122.77 \mathrm{~m}\end{aligned}$
If the diameter of wire is doubled, resistance will become $\frac{1}{4}$ th of the original (since $R \propto \frac{1}{A}$ or $R \propto \frac{1}{d^{2}}$ ).
Decrease of resistance will be $10-\frac{10}{4}=7.5 \Omega$

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Question 32 Marks

State reasons to explain these observations.
a. Our eye is more sensitive to yellow colour but even then danger signals are red in colour.
b. Violet colour is seen at the bottom of the spectrum when light is displaced by a prism.

Answer

a. An object is seen only when the light illuminating it is reflected and reach our eye. According to Rayleigh's scattering Law, the intensity of scattered light $\propto \frac{1}{\lambda^{4}}$. Since yellow colour has small wavelength than red colour, so scattering of yellow colour is more than the red colour. It means signal is illuminated more brightly by the red colour than the yellow colour. Hence, the signals can be seen easily from a longer distance. Therefore, red colour is used for danger signals than yellow colour.
b. In the visible spectrum, violet light have the shortest wavelength.Therefore, it has the highest refractive index. Therefore, when white light is passed through the prism, it split into its seven colours to give visible spectrum and violet colour having the shortest wavelength deviated the most.

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Science Answer the questions.[Phy-2M]

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