To find the transient time of a series RC circuit, we calculate the time constant ($\tau$). The time constant represents the time required for the capacitor's voltage to reach approximately 63.2% of its final value during charging or discharge.
Calculating RC Circuit Transient Time
The formula for the time constant ($\tau$) in an RC circuit is:
$ \tau = R \times C $
Where:
- $R$ is the resistance in Ohms ($\Omega$)
- $C$ is the capacitance in Farads (F)
Applying Given Values
We are given:
- Resistance, $R = 8 \, \text{kilo-Ohms} = 8 \times 10^3 \, \Omega$
- Capacitance, $C = 8 \, \text{mF} = 8 \times 10^{-3} \, \text{F}
Now, substitute these values into the formula:
$ \tau = (8 \times 10^3 \, \Omega) \times (8 \times 10^{-3} \, \text{F}) $
$ \tau = 64 \times 10^{(3 + (-3))} \, \Omega \cdot \text{F} $
$ \tau = 64 \times 10^0 \, \text{s} $
$ \tau = 64 \times 1 \, \text{s} $
$ \tau = 64 \, \text{s} $
Final Result
The transient time (time constant) of the series RC circuit is 64 seconds.
Important Questions from Time Constant
The time constant of an inductive circuit is defined as the time required for the circuit current to rise to _____ % (approximately) of its final steady state value.
Which of the following groups have similar units?
Symbols have their own common meanings.
Which of the following is/are not discharging equation/equations for an R-C circuit?
1. Capacitor voltage: \[ v_C = V_0 e^{-\tfrac{t}{RC}} \] 2. Resistor voltage: \[ v_R = E e^{-\tfrac{t}{RC}} \] 3. Discharging current: \[ i = \frac{V_0}{R} e^{-\tfrac{t}{RC}} \]
Select the correct answer using the code given below.
- Match the following Lists regarding time constant with capacitor discharging voltage:Select the correct answer using the code given below.
List-I (Time constant) List-II (Capacitor discharging voltage) P. $1\tau$ 1. 0.67% of E Q. $2\tau$ 2. 36.8% of E R. $3\tau$ 3. 13.5% of E S. $4\tau$ 4. 5% of E T. $5\tau$ 5. 1.87% of E What is the voltage across a capacitor after being charged from a 10 V DC source for a period of one time constant?
