Electric Transients: Solving RC Circuits Problems

  • Thread starter cunhasb
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In summary: Thank you so much guys!In summary, the capacitor will take approximately 160.94 microseconds to reach 20 volts after being connected to the resistor.
  • #1
cunhasb
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I would really appreciate if anyone could help me figure out these problems...

An RC circuit has a time constant of 40 microseconds. If the capacitor is first charged to a voltage of 80 volts and the RC circuit is then closed upon itself, after what time will the capacitor voltage be equal to 5 volts?... and

An RC circuit has a time constant of 0.0001 second. If the capacitor C is charged to 100 volts and, with the battery removed, the capacitor is then allowed to discharge through the resistor, at what time after being connected to the resistor will the voltage be 20 volts? (Assume that, in discharging, the voltage V at any time is equal to V=V(0) e^(-1/RC), where V(0) is the voltage to which C was charged.)

Thank you so much guys...
 
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  • #2
Can you write out the formula for voltage or charge as a function of time, given the time constant?

Then we can point you in the right direction if necessary.
 
  • #3
cunhasb said:
I would really appreciate if anyone could help me figure out these problems...

An RC circuit has a time constant of 40 microseconds. If the capacitor is first charged to a voltage of 80 volts and the RC circuit is then closed upon itself, after what time will the capacitor voltage be equal to 5 volts?... and

An RC circuit has a time constant of 0.0001 second. If the capacitor C is charged to 100 volts and, with the battery removed, the capacitor is then allowed to discharge through the resistor, at what time after being connected to the resistor will the voltage be 20 volts? (Assume that, in discharging, the voltage V at any time is equal to V=V(0) e^(-1/RC), where V(0) is the voltage to which C was charged.)

Thank you so much guys...
Your formula is independent ot the time. The correct formula would be:
[tex]V(t) = V(0)e^{-\frac{t}{RC}}[/tex]
Where [tex]RC[/tex] is the time constant. If you replace V(0) with the initial value of the voltage and V(t) with the final value, you can use logarithms to solve for the time [tex]t[/tex].
 
  • #4
Thank you so much guys...

well... I think I got it... correct me if I'm wrong...

1) Rc= 40 micro V(0) = 80 T=? V = 5V

V=v(0) e^(-t/RC)
5=80*e^(-t/RC)
5/80=e^(-t/RC)
RC*ln0.0625=-t
t=110.903 microseconds...

2) Rc= 0.0001 V(0) = 100 T=? V = 20V

V=v(0) e^(-t/RC)
20=100*e^(-t/RC)
20/100=e^(-t/RC)
RC*ln0.2=-t
t=160.94 microseconds...
 
  • #5
That's it.
 

FAQ: Electric Transients: Solving RC Circuits Problems

What is an electric transient?

An electric transient is a temporary change in the electric current or voltage in a circuit. It occurs when there is a sudden change in the circuit, such as turning it on or off, or when there is a change in the applied voltage. These transients can cause problems in circuits, and it is important to understand how to solve them.

What is an RC circuit?

An RC circuit is a circuit that contains a resistor (R) and a capacitor (C). These components work together to control the flow of electric current in the circuit. RC circuits are commonly used in electronic devices, such as filters and timing circuits, and are important to understand in the study of electric transients.

How do you solve RC circuit problems?

To solve RC circuit problems, you first need to understand the properties of resistors and capacitors. You can then use the equations V=IR and Q=CV to calculate the voltage and charge in the circuit. From there, you can use Kirchhoff's laws and other circuit analysis techniques to solve for any unknown variables. It is also helpful to use circuit simulation software to visualize and analyze the circuit.

What are some common types of electric transients in RC circuits?

Some common types of electric transients in RC circuits include the charging and discharging of capacitors, as well as the switching on and off of circuits. These transients can cause spikes or dips in voltage and current, which can affect the performance of electronic devices.

How can I prevent or minimize electric transients in RC circuits?

There are a few ways to prevent or minimize electric transients in RC circuits. One way is to use components with higher voltage and current ratings. Another way is to add a diode or other protective devices to the circuit. Additionally, proper circuit design and layout can help reduce the effects of transients. It is also important to regularly maintain and troubleshoot circuits to catch and fix any potential issues before they become bigger problems.

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