How Does Current Behave in a Discharging RC Circuit?

In summary: I_o = \frac{V_o}{R}##.In summary, the current flowing when the capacitor has been discharging for 5μs can be found using the equation Vc = Ve^-t/CR, where Vc is the voltage across the capacitor, V is the initial voltage, R is the resistance, and C is the capacitance. After substituting values, the current can be calculated to be approximately 0.156mA. Alternative methods, such as using the initial current and time constant, can also be used to find the current at 5μs.
  • #1
brenfox
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1

Homework Statement


Determine the current flowing when the capacitor has been discharging for 5μs
Capacitance=400 pico farads which is charged to 10v through a 50kΩ resistor.


Homework Equations


Vc = ve-t/CR


The Attempt at a Solution

So Vc =Ve -t/CR
-t/CR = -5*10^-6/400*10^-12*50*10^3
Which equals -0.25 so...
Vc= 10*e-0.25
Vc = 10*0.7788
Vc = 7.788 volts after 5 micro seconds

To find the current flowing after 5 micro seconds
i = Vr/R since Vr=Vc Vc/R = 7.788/50000 = 0.156mA.
Am i in the right ball park with this? Any guidance will be greatly appreciated.
 
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  • #2
brenfox said:

Homework Statement


Determine the current flowing when the capacitor has been discharging for 5μs
Capacitance=400 pico farads which is charged to 10v through a 50kΩ resistor.


Homework Equations


Vc = ve-t/CR


The Attempt at a Solution

So Vc =Ve -t/CR
-t/CR = -5*10^-6/400*10^-12*50*10^3
Which equals -0.25 so...
Vc= 10*e-0.25
Vc = 10*0.7788
Vc = 7.788 volts after 5 micro seconds

To find the current flowing after 5 micro seconds
i = Vr/R since Vr=Vc Vc/R = 7.788/50000 = 0.156mA.
Am i in the right ball park with this? Any guidance will be greatly appreciated.

Yup, looks fine.

You could also have written the expression for the current ##I(t) = I_o e^{-\frac{t}{\tau}}## using the initial current Io from the initial conditions.
 
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1. What is a transient RC circuit?

A transient RC circuit is an electrical circuit that contains a resistor (R) and a capacitor (C) connected in series. It is used to study the behavior of capacitors in circuits and how they respond to changes in voltage and current over time.

2. How does a transient RC circuit work?

In a transient RC circuit, the capacitor initially behaves as an open circuit, blocking the flow of current. As the circuit is turned on, the capacitor charges up until it reaches the same voltage as the source. This creates a flow of current through the resistor, causing the capacitor to discharge. This process continues until the capacitor reaches equilibrium.

3. What factors affect the behavior of a transient RC circuit?

The behavior of a transient RC circuit is influenced by several factors, including the resistance and capacitance values, the voltage source, and the time constant (RC) of the circuit. These factors determine the rate at which the capacitor charges and discharges, and the overall behavior of the circuit.

4. What is the time constant of a transient RC circuit?

The time constant (τ) of a transient RC circuit is the product of the resistance and capacitance values, represented by the equation τ = RC. It is a measure of how quickly the capacitor charges or discharges in the circuit. A larger time constant results in a slower rate of change in the circuit, while a smaller time constant leads to a faster rate of change.

5. What are some real-world applications of transient RC circuits?

Transient RC circuits have many practical applications, including in filters, signal processing, and timing circuits. They are also used in electronic devices, such as radios and televisions, to control the flow of current and voltage. Additionally, transient RC circuits are essential in the design and analysis of electronic circuits and systems in various industries, such as telecommunications, automotive, and aerospace.

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