This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
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Here are the answers to the questions from the image: 11. a. Define the following terms: i. Electrolysis: Electrolysis is the process of using electrical energy to drive a non-spontaneous chemical reaction. It involves passing an electric current through an electrolyte to decompose it. ii. Reactance: Reactance is the opposition to the change in current or voltage in an AC circuit due to inductance or capacitance. It is measured in ohms (). iii. Impedance: Impedance is the total opposition to current flow in an AC circuit, combining both resistance and reactance. It is a complex quantity, also measured in ohms (). iv. Eddy current: Eddy currents are localized electric currents induced within a conductor when it is exposed to a changing magnetic field. They flow in closed loops perpendicular to the magnetic field. 11. b. The current I in an a.c. circuit is represented by the equation I = 2.5 100 t . Sketch a variation of I with t. The graph of I versus t would be a sine wave. The amplitude of the current is 2.5 A. The period T = (2)/() = (2)/(100) = (1)/(50) = 0.02 s. The current starts at 0, increases to a maximum of 2.5 A at t = 0.005 s, returns to 0 at t = 0.01 s, decreases to a minimum of -2.5 A at t = 0.015 s, and returns to 0 at t = 0.02 s. . Determine the frequency of the current. Step 1: Compare the given equation with the standard form of an AC current equation, I = I_0 ( t). From I = 2.5 100 t, we have = 100 rad/s. Step 2: Use the relationship between angular frequency () and frequency (f). = 2 f 100 = 2 f Step 3: Solve for f. f = (100)/(2) f = 50 Hz The frequency of the current is 50 Hz. . Calculate the root mean square of the current. Step 1: Identify the peak current (I_0) from the equation. From I = 2.5 100 t, the peak current I_0 = 2.5 A. Step 2: Use the formula for RMS current (I_rms) for a sinusoidal waveform. I_rms = (I_0)/(sqrt(2)) Step 3: Substitute the value of I_0 and calculate. I_rms = (2.5)/(sqrt(2)) I_rms ≈ (2.5)/(1.4142) I_rms ≈ 1.7677 A The root mean square of the current is 1.77 A (to 3 significant figures). 11. c. Write down the relationship between refracting angle A of a triangle glass prism, the minimum deviation Dm and refractive index. The relationship for the refractive index () of a prism at minimum deviation is given by: = ((A + D_m)/(2))((A)/(2)) where A is the refracting angle of the prism and D_m is the angle of minimum deviation. 11. d. Show that the pressure on a single molecule of a gas inside a box is given by p = (1)/(3) c^2, where = density and C = speed. This formula represents the pressure exerted by an ideal gas, not a single molecule. Here's the derivation for the pressure of an ideal gas: Step 1: Consider a single molecule of mass m moving with velocity v_x in a cubical box of side length L. When it collides elastically with a wall perpendicular to the x-axis, its momentum changes by p_x = m(-v_x) - m(v_x) = -2mv_x. The time taken for the molecule to travel to the opposite wall and back is t = (2L)/(v_x). The force exerted by this molecule on the wall is F_x = (| p_x|)/( t) = (2mv_x)/(2L/v_x) = (mv_x^2)/(L). Step 2: For N molecules in the box, the total force on one wall is F = _i=1^N m v_xi^2L. The pressure P on the wall is P = (F)/(A) = (F)/(L^2) = (1)/(L^3) _i=1^N m v_xi^2. Since L^3 = V (volume of the box), P = (m)/(V) _i=1^N v_xi^2. Step 3: For a large number of molecules, the average of the square of the velocity components is equal in all directions: v_x^2 = v_y^2 = v_z^2. The mean square speed c^2 (or v^2) is given by c^2 = v_x^2 + v_y^2 + v_z^2 = 3v_x^2. So, v_x^2 = (c^2)/(3). Therefore, _i=1^N v_xi^2 = N v_x^2 = N (c^2)/(3). Step 4: Substitute this into the pressure equation. P = (m)/(V) (N (c^2)/(3)) P = (1)/(3) (Nm)/(V) c^2 Step 5: Recognize that Nm is the total mass of the gas, and (Nm)/(V) is the density () of the gas. P = (1)/(3) c^2 This shows that the pressure exerted by an ideal gas is given by P = (1)/(3) c^2. Drop the next question.