Question

Two identical capacitors are connected as shown and have an initial charge of Q₀. The separation between the plates of each capacitor is d₀. Suddenly the left plate of the upper capacitor and right plate of the lower capacitor start moving with speed v towards the left while the other plate of each capacitor remains fixed. `("given" (Q_0V)/(2d_0) = 10 A)`. The value of current in the circuit is ______ A.

 

Options

• 10.00

• 20.00

• 30.00

• 40.00

Answer 1

Two identical capacitors are connected as shown and have an initial charge of Q₀. The separation between the plates of each capacitor is d₀. Suddenly the left plate of the upper capacitor and right plate of the lower capacitor start moving with speed v towards the left while the other plate of each capacitor remains fixed. `("given" (Q_0V)/(2d_0) = 10 A)`. The value of the current in the circuit is 20.00 A.

Explanation:

`q_1/C_1 = q_2/C_2`

`q_1 + q_2 = 2Q_0`

`C_1 = (epsilonA)/(d_0 + Vt), C_2 = (epsilonA)/(d_0 - Vt)`

`q_1/q_2 = (d_0 - Vt)/(d_0 + Vt)`

⇒ `q_1 + q_2((d_0 - Vt)/(d_0 + Vt)) = 2Q_0`

⇒ `q_2((2d_0)/(d_0 + Vt)) = 2Q_0`

`muq_2 = (2Q_0)/(2d_0)(d_0 + Vt)`

I = `(dq_2)/(dt) = (Q_0V)/(d_0)` = 20A