Question

At a moment (t = 0), when the charge on capacitor C₁ is zero, the switch is closed. If I₀ be the current through inductor at t = 0, for t> 0 (initially C₂ is uncharged)

• A. Maximum current through inductor equals I₀/2
• B. Maximum current through inductor equals $\frac{C_{1}I_{0}}{C_{1} + C_{2}}$
• C. Maximum charge on C₁ = $\frac{C_{1}I_{0}\sqrt{LC_{2}}}{C_{1} + C_{2}}$
• D. Maximum charge on C₁ = $C_{1}I_{0}\sqrt{\frac{L}{C_{1} + C_{2}}}$

Answer 1

Answer: (D)

Maximum charge on C₁ = $C_{1}I_{0}\sqrt{\frac{L}{C_{1} + C_{2}}}$

Answer 2

Maximum current through the inductor is I₀.

Maximum charge = ?

By conservation of energy

$\frac { 1 } { 2 }$ LI₀² =$\frac { 1 } { 2 }$ (C₁ + C₂)V²

V = I₀

Q₁ = C­₁V = C₁I₀ $\sqrt { \frac { L } { \mathrm { C } _ { 1 } + \mathrm { C } _ { 2 } } }$