The differential coefficient of the \( \sin(x^2 + 5) \) with respect to \( x \) will be:
Two parallel plate capacitors of capacitances \( C \) and \( 2C \) are joined with a battery of voltage difference \( V \) as shown in the figure. If the battery is removed and the space between the plates of the capacitor of capacitance \( C \) is completely filled with a material of dielectric constant \( K \), then find out:
Differentiate between interference and diffraction of light. Explain qualitatively the diffraction phenomenon of light by a single slit. Light of 6000 Ã… wavelength is incident normally on a single slit of width \( 3 \times 10^{-4} \, \text{cm} \). Find out the angular width of the central maxima.
Show that the circumference of the orbit of an electron revolving in the \( n \)-th orbit is equal to \( n\lambda \) with the help of Bohr's quantum theory. Also, show the emission and absorption spectral lines between energy levels \( n = 1 \) and \( n = 3 \) of hydrogen atom.
What do you mean by the current sensitivity of a moving coil galvanometer? Resistance of a galvanometer is \( 50 \, \Omega \) and for full-scale deflection, the current is \( 0.05 \, \mathrm{A} \). What would be the required length of a wire to convert it into an ammeter of 5 A range? (Area of cross-section of wire = \( 2.7 \times 10^{-6} \, \mathrm{m^2} \), specific resistance of the wire material = \( 5.0 \times 10^{-7} \, \Omega \cdot \mathrm{m} \))