Electric currents which vary for a small finite time, while growing from zero to maximum or whil...
0Electric currents which vary for a small finite time, while growing from zero to maximum or while decaying from maximum value to zero value are called transient currents.
Helmholtz equation for growth of current in \( L R \) circuit is \( I=I_{0}\left(1-e^{-\frac{R}{L} t}\right)=I_{0}\left(1-e^{-t / \tau}\right) \),
where \( \tau=\frac{L}{R} \) is called inductive time constant of
FIGURE \( 7.7 \)
Again, discharging of a capacitor through a
\( L R \) circuit. Again, Helmholtz equation for decay of resistor is represented as
current in \( L R \) circuit
\[
I=\left(I_{0} e^{-\frac{R}{L} t}\right)=I_{0} e^{-t / \tau}
\]
\[
q=q_{0} e^{-t / R C}=q_{0} e^{-t / \tau}
\]
The charging and discharging of a capacitor through a resistance is shown in Fig. 7.8.
Clearly, smaller the time constant, faster are the growth as well as decay of current in \( R L \) circuit. The reverse is also true. The growth and decay of current in \( R L \) circuit are shown in Fig. 7.7.
Again, charging of a capacitor through a resistor is represented by \( q=q_{0}\left(1-e^{-t / R C}\right)=q_{0}\left(1-e^{-t /} \tau\right) \)
where \( \tau=R C= \) capacitative time constant of \( R C \) circuit.
FIGURE \( 7.8 \)
Note that inductive time constant of \( R L \) circuit is the time in which current in \( R L \) circuit grows to \( 63.2 \% \) of the maximum value of current or It is the time in which current in \( R L \) circuit decays to \( 36.8 \% \) of the maximum value of current.
Similarly, capacitative time constant of \( R C \) circuit is the time in which charge on the capacitor grows to \( 63.2 \% \) of the maximum charge or It is also the time in which charge on the capacitor decreases to \( 36.8 \% \) of the maximum value of charge.
Read the above passage carefully and answer the following questions on the basis of your understanding of this passage and related studied concepts.
What is the equation of charging of a capacitor through a resistance?
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