In the circuit shown, the symbols have their usual meanings. The cell has emf E. X is initially joined to Y for a long time. Then, X is joined to Z. The maximum charge on C at any later time will be

Question

In the circuit shown, the symbols have their usual meanings. The cell has emf E. X is initially joined to Y for a long time. Then, X is joined to Z. The maximum charge on C at any later time will be (A) (E/R √ LC) (B) (E R/2 √ LC) (C) (E √ LC/2R) (D) (E √ LC/R)

Tardigrade Admin · Accepted Answer

Current in inductor =(E/R) ∴ its energy =(1/2) (L E2/R2) Same energy is later stored in capacitor (Q2/2 C)=(1/2) (L E2/R2) ⇒ Q=(√L C/E) (E/R)

Q. In the circuit shown, the symbols have their usual meanings. The cell has emf $E$ . $X$ is initially joined to $Y$ for a long time. Then, $X$ is joined to $Z$ . The maximum charge on $C$ at any later time will be

$\frac{E}{R L C}$

$\frac{ER}{2 L C}$

$\frac{E L C}{2 R}$

$\frac{E L C}{R}$

Current in inductor $= \frac{E}{R}$
$∴$ its energy $= \frac{1}{2} \frac{L E ^{2}}{R ^{2}}$
Same energy is later stored in capacitor
$\frac{Q ^{2}}{2 C} = \frac{1}{2} \frac{L E ^{2}}{R ^{2}}$
$\Rightarrow Q = \frac{L C}{E} \frac{E}{R}$

Q. In the circuit shown, the symbols have their usual meanings. The cell has emf E. X is initially joined to Y for a long time. Then, X is joined to Z. The maximum charge on C at any later time will be

RLC​E​

2LC​ER​

2RELC​​

RELC​​