Charge & discharge of a condenser

Charge & discharge of a condenser

Charge of a condenser

(1) The capacitor takes some finite time in the charging process.

(2) The quantity of charge at any instant of time t is given by q = q₀[1–e^–t/RC]

i.e. the charge falls exponentially.

Where $q_0$ = Maximum final value of charge at t = $\infty$

R = Resistance of whole circuit

(3) If t = RC = $\tau$, then

q = q₀ [1 – e–(RC/RC)]

= q₀ $\left[1-\frac{1}{e}\right]$

= q₀ (1 – 0.37)

= 0.63 q₀ [$\because$ e = 2.73 $\Rightarrow$ 1/e = 0.37]

= 63% of q₀.

(4) Time t = RC is known as time constant i.e. the time constant is that time during which the charge rises on the condenser plates to 63% of its maximum value during charging process or falls to 37% of its maximum value during discharge process.

(5) The potential difference across the condenser plates any instant of time is given by

V = V0 [1 – e^–(t/RC)] volt

(6) The potential curve is also similar to that of charge. During charging process an electric current flows in the circuit for a small interval of time which is known as the transient current. The value of this current at any instant t is given by I = I₀e^–(t/RC) amp.

(7) If t = RC = $\tau$ = Time constant

I = I₀ e^–(RC/RC) = $\frac{I_0}{e}$ = 0.37I₀ = 37% of I₀

i.e. time constant is that time during which current in the circuit falls to 37% of its maximum value.

Discharge of a condenser

(1) The capacitor takes some finite time in the discharging process.

(2) The quantity of charge on the condenser at any instant of time is given by q = q₀e^–(t/RC) i.e. the charge falls exponentially.

(3) If t = RC = $\tau$ = time constant,

q = q₀/e = 37% q₀

i.e. the time constant is that time during which the charge

on condenser plates during discharge process falls to 37% of it's maximum value.

(4) The dimensions of RC are those of time

i.e. M⁰L⁰T¹ and dimension of $\frac{1}{RC}$ are those of frequency i.e. M⁰L⁰T^–1

(5) The potential difference across the condenser any instant of time is given by

V = V0 e–(t/RC) volt

(6) The transient current at any instant of I = –I0e–(t/RC) amp.

i.e. the current in the circuit in the circuit decreases exponentially but its direction is opposite to that of charging current.