Class-XII Physics:Transient Current

Growth and decay of current in LR circuit

212

Growth of current

1 and 2 are connected
213
  • Current through circuit at any time t
  1. At t =0, I = 0
  2. At t = ∞ , I = Io = (Vo/R)
  3. At any time t,
CodeCogsEqn (70)
where, τ = (L/R) = Inductive time constant
Io = maximum value of current in the circuit
At t = (L/R) ,
CodeCogsEqn (71)
  • Voltage across Inductor (L) at any time t
  1. At t =0, V = Vo
  2. At t = ∞ , Vo = 0
  3. At any time t,
CodeCogsEqn (72)
214
  • Energy stored in inductor at any time t
  1. At t =0, U = 0
  2. At t = ∞ , CodeCogsEqn (68) = Uo
  3. At any time t,
CodeCogsEqn (73)
  • Heat produced in resistance in time t
CodeCogsEqn (74)

Decay of Current

218
1 and 3 are connected.
  • Current through circuit at any time t
  1. At t =0, I = Io = (Vo/R)
  2. At t = ∞ , I = 0
  3. At any time t,
CodeCogsEqn (75)
where, τ = (L/R) = Inductive time constant
At t = (L/R) ,
CodeCogsEqn (71)
Inductive time constant of RL circuit is defined as the time during which the current in the circuit falls from maximum value to 0.368 times the maximum value of current.
  • Voltage across Inductor (L) at any time t
CodeCogsEqn (72)
215
  • Energy remain in inductor (L) at any time t
  1. At t =0, CodeCogsEqn (68) = Uo
  2. At t = ∞ , U = 0
  3. At any time t,
CodeCogsEqn (76)
  • Heat produced in resistance (R) in time t
CodeCogsEqn (74)  = Uo – U

Charging & discharging of a capacitor in RC circuit

216

Charging of a capacitor in RC circuit

1 and 2 are connected
217
  • Charge at any instant
CodeCogsEqn (77)
τ = RC = Capacitive time constant
Qo = maximum value of charge
Capacitive time constant of RC circuit is defined as the time during which the charge in the capacitor grows to 0.632 times the maximum value of charge.
  • Voltage across the capacitor during charging in RC circuit
CodeCogsEqn (78)
  • Current in RC circuit at any instant during the charging of the capacitor
CodeCogsEqn (79)
Io = maximum value of current in the circuit
220

Discharging of a capacitor or decay of charge in RC circuit

1 and 3 are connected
219
  • Charge at any instant
CodeCogsEqn (82)
Qo = maximum value of charge
  • Voltage across the capacitor during discharging in RC circuit
CodeCogsEqn (81)

  • Current in RC circuit at any instant during the discharging of the capacitor
CodeCogsEqn (80)
Io = maximum value of current in the circuit
221

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