Question

In an oscillating LC circuit the maximum charge on the capacitor is The charge on the capacitor when the energy is stored equally between the electric and magnetic field is

• A. $Q/2$
• B. $Q/ \sqrt {2}$
• C. $Q/ \sqrt {3}$
• D. $Q$

Answer 1

Answer: (B)

$Q/ \sqrt {2}$

Answer 2

Total energy stored $=\frac{1}{2} \frac{Q^{2}}{C}$ At any time electrostatic energy is equal to magnetic energy. $\frac{1}{2} \frac{ Q ^{2}}{ C }=\frac{1 q ^{2}}{2}+\frac{1}{2} LI ^{2}$ ..(1) Since $\frac{ q ^{2}}{2 C }=\frac{ LI ^{2}}{2}$ Equation (1) becomes, $\frac{1 Q^{2}}{2} \frac{q^{2}}{C}=\frac{q}{C}$ $q=\frac{Q}{\sqrt{2}}$ Where $q$ is the charge on capacitor at this instant.