In oscillating LC circuit, the total stored energy is U and maximum charge upon capacitor is Q . When the charge upon the capacitor is (Q/2), the energy stored in the inductor is

Question

In oscillating LC circuit, the total stored energy is U and maximum charge upon capacitor is Q . When the charge upon the capacitor is (Q/2), the energy stored in the inductor is (A) (U/2) (B) (U/4) (C) (4/3) U (D) (3 U/4)

Tardigrade Admin · Accepted Answer

Initial energy = total energy =(Q2/2 C)=U U'=(Q2/4(2 C)) (. as .Q'=(Q/2)) =(Q2/8 C) U text inductor =U text total -U text capacitor =(Q2/2 C)-(Q2/8 C) =(3 Q2/8 C)=(3/4) U

Q. In oscillating LC circuit, the total stored energy is $U$ and maximum charge upon capacitor is $Q .$ When the charge upon the capacitor is $\frac{Q}{2}$ , the energy stored in the inductor is

$\frac{U}{2}$

$\frac{U}{4}$

$\frac{4}{3} U$

$\frac{3 U}{4}$

Initial energy $=$ total energy
$= \frac{Q ^{2}}{2 C} = U$
$U^{'} = \frac{Q ^{2}}{4 ( 2 C )}$
$($ as $Q^{'} = \frac{Q}{2})$
$= \frac{Q ^{2}}{8 C}$
$U_{inductor} = U_{total} - U_{capacitor}$
$= \frac{Q ^{2}}{2 C} - \frac{Q ^{2}}{8 C}$
$= \frac{3 Q ^{2}}{8 C} = \frac{3}{4} U$

Q. In oscillating LC circuit, the total stored energy is U and maximum charge upon capacitor is Q. When the charge upon the capacitor is 2Q​, the energy stored in the inductor is

2U​

4U​

34​U

43U​