
The circuit for studying the V-I characteristics of a p-n junction diode typically includes:
- A variable DC power supply to provide different values of voltage \( V \),
- A p-n junction diode,
- A series resistor to limit the current through the diode, and
- A voltmeter and ammeter to measure the voltage across and the current through the diode, respectively.
Here is a simple diagram: \[ \begin{array}{c} \text{DC Power Supply} \quad \longrightarrow \quad \text{Series Resistor} \quad \longrightarrow \quad \text{P-N Junction Diode} \quad \longrightarrow \quad \text{Ammeter} \quad \longrightarrow \quad \text{Voltmeter} \end{array} \] The current and voltage are varied, and the corresponding V-I characteristics are plotted.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).