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Resonance occurs whenever the phase angle of the circuit is zero, The only way that f = 0 is if XL = XC Note that tanϕ = \(\frac{ X }{ R}\) where X = reactance and ϕ = angle of lead or lag. therefore, tan ϕ = \(\frac{ X_L - X_C}{ R}\) but at resonance \(X_L = X_C\) tan ϕ = \(\frac{0}{R}\) = 0 and ϕ = \(tan^{-1}\) = 0º

∆E = hf f = (∆E)/h = (5.44 x 10-19)/6.6 x 10-34 = 8.24 x 1014

transistor serve the same purpose as triode valve, which is amplification of signals.

A semiconductor is a material whose conductivity is between good conductor and insulator. Example of pure semi conductors are silicon and germanium

(1)/v + (1)/u = (1)/f (1)/v + (1)/15 = (1)/5 (1)/v = (1)/5 - (1)/15 = (3 - 1)/15 = (2)/15 ∴ v = (15)/2 = 7.5 cm magnification = (v)/u = (image size)/object size (7.5)/15 = (X)/4 ∴ image size. X = (7.5 x 4)/15 = 2 cm

Refraction index, n = (real depth)/apparent depth 1.5 = (10)/X X = (10)/1.5 = 6.67 cm

Dispersion is the splitting of white light into its spectral component colors and is caused by different speed of the colors in the prism.

refractive index(n) = \(\frac{sin i}{sinr}\) where r = 180-(90+i) → r=90-i since sin(90-i)=cos i : refractive index(n) = \(\frac{sin i}{cos i}\) → tan i

Sound wave requires a material medium for its propagation. so when air is being pumped out the density of the medium is being reduced and the sound dies down. when all the air has been pumped out of the glass, no sound will be heard, as sound sound cannot travel through vacuum

The lengthening effect of sound is known as reverberation.

The retina is light sensitive layer living the inner wall of the eye where image is formed. in the camera, image is formed on a light sensitive film.

Concave lens diverges parallel rays of light. A short sighted person has the image formed before the retina,and the rays have to be diverged so that they intersect to form image onto the retina

- Alpha radiation consists of helium- He\(^{4}_{2}\) 2 Alpha decay --> 2 X He\(^{4}_{2}\) = Element\(^{8}_{4}\) - Beta particles are high energy electrons- e\(^{0}_{-1}\) 3 Beta particles --> 3 X e\(^{0}_{-1}\) = Element\(^{0}_{-3}\) - Gamma rays are waves of electromagnetic energy, or photons. the mass and atomic number of the resulting element = U\(^{235}_{92}\) - Elements( \(^{8}_{4}\) + \(^{0}_{-3}\) ) --> Element\(^{227}_{91}\)

The container is filled 'only with ice' to the brim (no liquid water mentioned). Ice is less dense than water (it expands when freezing). When the ice melts, the same mass turns into water that occupies less volume. Result: The water level drops below the brim.

Dew point is the temperature at which the water vapour present in air is just sufficient to saturate it. Dew is formed when air is cooled below its dew point