If capacitance of L-C parallel circuit is made four times then f=_

Explanation

We are given that initially a LC circuit has resonant frequency f. If initial capacitance is C and initial inductance is L then the expression for resonant frequency can be written asf=1/2π (underroot) LC.Now, the capacitance of the coil has increased 4 times. The new capacitance is given as C′=4CThe inductance is independent of capacitance and remains same, therefore,L′=LBut the resonant frequency changes because it is dependent on capacitance of the coil. The expression for new resonant frequency can be written as f′=1/2π (underroot) L'C' Substituting the values of L' and C', we getf′=1/ 2π√L* 4C 1/2 * 1/2pi * √LCUsing equation (i) here, we getf′=f/2 Therefore, the resonant frequency becomes half on increasing the capacitance four times.