Assertion (A): The deflection in a galvanometer is directly proportional to the current passing through it.
Reason (R): The coil of a galvanometer is suspended in a uniform radial magnetic field.
Galvanometer:
A galvanometer is an instrument used to show the direction and strength of the current passing through it. In a galvanometer, a coil placed in a magnetic field experiences a torque and hence gets deflected when a current passes through it.
The name "galvanometer" is derived from the surname of Italian scientist Luigi Galvani, who in 1791 discovered that electric current makes a dead frog’s leg jerk.
A spring attached to the coil provides a counter torque. In equilibrium, the deflecting torque is balanced by the restoring torque of the spring, and we have the relation:
\[ NBAI = k\phi \]
Where:
As the current \( I_g \) that produces full-scale deflection in the galvanometer is very small, the galvanometer alone cannot be used to measure current in electric circuits.
To convert a galvanometer into an ammeter (to measure larger currents), a small resistance called a shunt is connected in parallel to the galvanometer.
To convert it into a voltmeter (to measure potential difference), a high resistance is connected in series with the galvanometer.
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 \(P,O,Q\).