Explanation:
Data provided:
Area A = 10 cm×2 cm = 20×10⁻⁴ m²
Separation distance d between the plates = 1 mm = 1×10⁻³ m
Battery voltage, or emf = 100 V
Resistance = 1025 ohm
Solution:
In an RC circuit, the voltage across the plates varies with time t. At the outset, the voltage matches that of the battery, V₀ = emf = 100V. However, after a certain time t, both the resistance and capacitance alter this, leading to a final voltage V expressed as
Applying the natural logarithm to both sides,
(1)
Next, we can determine the capacitance using the plates' area.
C = ε₀A/d
= 
= 18×10⁻¹²F
We can now find the time it takes for the voltage to drop from 100 to 55 V by substituting C, V₀, V, and R values into equation (1)
= -(1025Ω)(18×10⁻¹² F) ln( 1 - 55/100)
= 15×10⁻⁹s
= 15 ns
The intensity of the sound increases because sound waves are mechanical waves, meaning they cannot move through a vacuum and require a medium to propagate.
The rocket's acceleration is described here as
now recognizing that
we integrate both sides
given that the rocket is accelerating for a duration of t = 10 s
thus, we have
consequently, after t = 10 s, the rocket will achieve a speed of 130 m/s in an upward direction
We will utilize Wien's displacement law, given by the equation λ T = b, where λ represents the wavelength of emitted light from a heated object at maximum. By substituting the provided temperature and constant b into the equation, we find λ for various temperatures: at 500 K, λ = 5.796 μm or 5796 nm; at 1050 K, λ = 2760 nm; at 1800 K, λ = 1610 nm; and at 2500 K, λ = 1159.2 nm. The visible light spectrum starts at 740 nm, suggesting that at 2500 K, some visible red light may emerge as its calculated peak wavelength is within the visible range.
