Advertisements
Advertisements
Question
A parallel plate capacitor (A) of capacitance C is charged by a battery to voltage V. The battery is disconnected and an uncharged capacitor (B) of capacitance 2C is connected across A. Find the ratio of total electrostatic energy stored in A and B finally and that stored in A initially.
Advertisements
Solution
The electric field in the region between the plates depends on the change given to the conducting plates,
For capacitor 'A' of capacitance C, having voltage V, the charge on it is given by Q = CV.
On connecting this capacitor A with capacitor B changes get distributed.
The total electrostatic energy stored in A is given by
`U_A = 1/2CV^2 = 1/2 Q^2/C` .........(i)
Since capacitor B is connected across capacitor A.
∴ `C_"net" = C_A + C_B`
= C + 2C
= 3C
∴ Total electrostatic energy in A and B is given by
`U_"net" = 1/2 Q^2/C_"net"`
= `1/2(Q^2/(3C))` ....(since total change Q remains constant)
= `1/3(1/2 Q^2/C)`
= `1/3U_A` .....[By equation (i)]
`U_"net"/U_A = 1/3`
APPEARS IN
RELATED QUESTIONS
A 12 pF capacitor is connected to a 50 V battery. How much electrostatic energy is stored in the capacitor?
In the following arrangement of capacitors, the energy stored in the 6 µF capacitor is E. Find the value of the following :
(i) Energy stored in 12 µF capacitor.
(ii) Energy stored in 3 µF capacitor.
(iii) Total energy drawn from the battery.
Find the charge on the capacitor shown in the figure.
The plates of a capacitor of capacitance 10 μF, charged to 60 μC, are joined together by a wire of resistance 10 Ω at t = 0. Find the charge on the capacitor in the circuit at (a) t = 0 (b) t = 30 μs (c) t = 120 μs and (d) t = 1.0 ms.
How many time constants will elapse before the current in a charging RC circuit drops to half of its initial value? Answer the same question for a discharging RC circuit.
How many time constants will elapse before the charge on a capacitors falls to 0.1% of its maximum value in a discharging RC circuit?
A capacitance C charged to a potential difference V is discharged by connecting its plates through a resistance R. Find the heat dissipated in one time constant after the connections are made. Do this by calculating ∫ i2R dt and also by finding the decrease in the energy stored in the capacitor.
Consider the situation shown in figure. The switch is closed at t = 0 when the capacitors are uncharged. Find the charge on the capacitor C1 as a function of time t.
A capacitor is a device that stores ____________.
A parallel plate condenser is immersed in an oil of dielectric constant 2. The field between the plates is ______.
