Home
Class 12
PHYSICS
In a circuit shown in fig. the capacitan...

In a circuit shown in fig. the capacitance of each capacitor is equal to `C` and the resistance, to `R` One of the capacitor was connected to a voltage `V_(0)` and then at the moment `t = 0` was shorted by means of the swich `Sw`. Find:
(a) a current `I` in the circuit as a function of time `t`:
(b) the amount of generated heat provided a dependence `I(t)` is known.

Text Solution

Verified by Experts

The correct Answer is:
(a) `I = (V_(0))/(R ) e^(-2t//Rc)`; (b) `(1)/(4)CV_(0)^(2)`
(a) Let charge on capacitor is `q` at time `t` Applying loop law

`(CV-q)/(C )-iR -(q)/(C ) = 0`
`(CV-2q)/(C ) =iR`
`(CV-2q)/(RC) = (dq)/(dt)`
`overset(q)underset(o)(overset(`)O)(dq)/(CV-2q)=overset(t)underset(0)(overset(')O)(dt)/(RC)Þ q = (CV)/(2) (1-e^(2t//RC))`
since `i = (dq)/(dt) = (V)/(R ) (1-e^(-2t//RC))`
(b) at final condition `V' = (CV)/(2C) = (V)/(2)`
`U_(i) = (1)/(2)CV^(2)`
`U_(f) = 2xx(1)/(2)C ((V)/(2))^(2) = (1)/(2)CV^(2)`

`H = DeltaU = (1)/(2)CV^(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

In the given circuit, one of the capacitors was connected to a voltage V_(0) and then at the moment t = 0 was shorted by means of the switch. Find the amount of heat generated.

An oscillating circuit consists of a capacitor with capacitance C , a coil of inductance L with negligible resistance, and aswitch. With the switch disconnected , the capacitor was charged to a voltage V_(m) and then at the moment t=0 the switch was closed . Find : (a) the current (I(t)) in the circuit as a function of time, (b) the emf of self- inductance in the coil at the moments when the electric energy of the capacitor is equal to that of the current in the coil.

Find the charge of each capacitor in the circuit shown in Fig.

A circuit consisting of a capacitor with capacitance C and a resistance R connected in series was connected at the moment t=0 to a source of ac voltage V=V_(m) cos omegat . Find the current in the circuit as a function of time t .

An electric circuit shown in figure has a negligibly small active resistance. The left - hand capacitor was charged to a voltage V_(0) and then at the moment t=0 the switch Sw was closed. Find the time dependence of the voltages in left and right capacitors.

A coil with active resistance R and inductance L was connected at the moment t=0 to a source of voltage V=V_(m)cos omegat. Find the current in the coil as a function of time t .

In the circuit shown, a capacitor charged to a potential difference V_(0) is connected to an uncharged capacitor through a resistor at t=0 , by closing the switch. Find current in the circuit as function of time. .

32 capacitor are connected in a circuit as shown in the figure. The capacitance of each capacitor is 3muF . Find equivalent capacitance across AB in muF .