Let $$\ell $$, r, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of $${\ell \over {rCV}}$$ in SI units will be :

In the above circuit, C = $${{\sqrt 3 } \over 2}$$$$\mu $$F, R₂ = 20 $$\Omega $$, L = $${{\sqrt 3 } \over {10}}$$ H and R₁ = 10 $$\Omega $$. Current in L-R₁ path is I₁ and in C-R₂ path it is I₂ . The voltage of A.C. source is given by, V = 200 $${\sqrt 2 }$$ sin (100 t) volts . The phase difference between I₁ and I₂ is :

A simple harmonic motion is represented by :

y = 5 (sin 3 $$\pi $$ t + $$\sqrt 3 $$ cos 3 $$\pi $$t) cm

The amplitude and time period of the motion are :

In the circuit shown, find C if the effective capacitance of the whole circuit is to be 0.5 $$\mu $$F. All values in the circuit are in $$\mu $$F.