Transient Behavior of Capacitor Pamalhin nga Pagkakataon sa Capacitor

Pagkini nga adunay voltage ang gihatag sa usa ka capacitor, ang mga elektron mubo sa pinaghulugan ngadto sa capacitor ug balik sa pinaghulugan. Sa ubang panahon, ang pag-akumula sa kargado sa capacitor magsugod agad. Tungod kay ang kargado sa capacitor nadaghan, ang voltage nga nahimo sa capacitor usab nadaghan. Ang voltage nga nahimo sa capacitor mag-abot sa supply voltage samtang ang rate sa pag-akumula sa kargado sa capacitor mapalit. Pagka ang duha ka voltage sama, walay labi nga pagtubig sa kargado gikan sa pinaghulugan ngadto sa capacitor. Ang pagtubig sa elektron gikan sa pinaghulugan ngadto sa capacitor ug balik sa pinaghulugan wala nay lain kon electric current.

Sa unang bahin, ang kuryente kini mahimong maximum ug human sa pipila ka oras ang kuryente makuha zero. Ang duration diin nagbag-o ang kuryente sa capacitor gitawag og transient period. Ang phenomenon sa charging current o uban pang electrical quantities sama sa voltage, sa capacitor gitawag og transient.
Para maintindohan ang transient behavior of capacitor atong i-draw ang RC circuit as shown below,

Karon, kon ang switch S is suddenly closed, ang kuryente magsugod nga moglow sa circuit. Atong current sa bisan unsang instant is i(t).
Also consider the voltage developed at the capacitor at that instant is Vc(t).
Hence, by applying Kirchhoff’s Voltage Law, in that circuit we get,

Now, if transfer of charge during this period (t) is q coulomb, then i(t) can be written as
Therefore,

Putting this expression of i(t) in equation (i) we get,

Now integrating both sides with respect to time we get,

Where, K is a constant can be determined from initial condition.
Let us consider the time t = 0 at the instant of switching on the circuit putting t = 0 in above equation we get,

There will be no voltage developed across capacitor at t = 0 as it was previously unchanged.
Therefore,

Now if we put RC = t at above equation, we get

This RC or product of resistance and capacitance of RC series circuit is known as time constant of the circuit. So, time constant of an RC circuit, is the time for which voltage developed or dropped across the capacitor is 63.2% of the supply voltage. This definition of time constant only holds good when the capacitor was initially unchanged.
Again, at the instant of switching on the circuit i.e. t = 0, there will be no voltage developed across the capacitor. This can also be proved from equation (ii).

So initial current through the circuit is, V/R and let us consider it as I0.
Now at any instant, current through the circuit will be,

Now when, t = Rc the circuit current.

So at the instant when, current through the capacitor is 36.7% of the initial current, is also known as time constant of the RC circuit.
The time constant is normally denoted will τ (taw). Hence,

Transient During Discharging a Capacitor

Karon, supuson ang capacitor fully charged, i.e. ang voltage sa capacitor sama sa voltage sa pinaghulugan. Kini nga ang voltage source disconnected ug instead ang duha ka terminals sa battery short circuited, ang capacitor magsugod sa discharging means, unequal distribution of electrons between two plates will be equalized through the short circuit path. The process of equaling electrons concentration in two plates will continue until the voltage at capacitor becomes zero. This process is known as discharging of capacitor. Now we will examine the transient behavior of capacitor during discharging.

Karon, gikan sa circuit hini, by applying Kirchhoff Current Law, we get,