Calculating Time Until Voltage Falls in a Circuit with Resistor and Capacitor

In summary, the conversation discusses the behavior of a charged capacitor in a circuit containing a switch, resistor, emf, and capacitor in series. The relevant equations for calculating the time constant and final voltage are mentioned. The speaker is unsure if logarithms are necessary to solve the problem. Another question is posed about the behavior of a bulb in a circuit with a switch, capacitor, and bulb in series. The speaker believes the bulb will have a delay before emitting light and will gradually get brighter as the capacitor charges. They ask for confirmation if this is correct.
  • #1
SMUDGY
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If a charged capacitor c=35 micro farads is connected to a resistor R=120 ohms how much time will elapse until the voltage falls to 10^6/D of its original max value?

Ciruit contains a switch, resistor, emf and a capacitor in series.

Relevant equations are Time constant= T=cR and V(Final)=V(initial) e^-t/cr


I think it requires logarithms but i am not sure.

Can you please help me how to answer this.
 
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  • #2
Another question is:

A circuit containing a switch, Vo, a capacitor and a bulb in series.

The capacior is originally uncharged. Describe the behaviour of the bulb from the instant the switch is on until a long time later.

I think there will be a delay for the bulb to emit light and then it will emit light getting slowly brighter as the capacitor is getting charged up.

Is this right?
 
  • #3


I would first clarify the question and gather all necessary information. It seems that the question is asking for the time it takes for the voltage to decrease to a certain percentage of its initial value in a circuit containing a resistor and capacitor in series. The relevant equations provided are correct and can be used to solve the problem.

To calculate the time constant (T), we can use the equation T = cR, where c is the capacitance and R is the resistance. In this case, T = (35 micro farads)(120 ohms) = 4.2 milliseconds.

Next, we can use the equation V(final) = V(initial) e^(-t/CR) to find the voltage at any given time (t). In this case, we are given that V(final) = 10^6/D of the initial voltage, where D is a constant. So, we can rewrite the equation as 10^6/D = V(initial) e^(-t/CR).

To solve for time (t), we can use logarithms. Taking the natural logarithm of both sides, we get ln(10^6/D) = ln(V(initial) e^(-t/CR)). Using logarithm rules, we can rewrite this as ln(10^6/D) = ln(V(initial)) - t/CR. Rearranging the equation, we get t = -CR ln(10^6/D) + CR ln(V(initial)). Plugging in the values, t = -4.2 milliseconds ln(10^6/D) + 4.2 milliseconds ln(V(initial)).

Therefore, the time it takes for the voltage to decrease to 10^6/D of its initial value is -4.2 milliseconds ln(10^6/D) + 4.2 milliseconds ln(V(initial)). This can be calculated using a calculator or a computer program. It is important to note that the value of D must be specified in order to get a specific time value.

In conclusion, using the given equations and logarithms, we can accurately calculate the time it takes for the voltage to decrease in a circuit with a resistor and capacitor in series. It is important to fully understand the problem and use appropriate equations and techniques to solve it.
 

1. How do I calculate the time until voltage falls in a circuit with a resistor and capacitor?

To calculate the time until voltage falls in a circuit with a resistor and capacitor, you can use the formula t = RC, where t is the time in seconds, R is the resistance in ohms, and C is the capacitance in farads.

2. What units should I use when calculating the time until voltage falls?

The units used in the formula t = RC are seconds for time, ohms for resistance, and farads for capacitance. Make sure to use consistent units for accurate calculations.

3. Can I use this formula for any circuit with a resistor and capacitor?

Yes, this formula can be used for any circuit with a resistor and capacitor, as long as the circuit is a simple series circuit and the capacitor is fully discharged at the start of the calculation.

4. What are some factors that may affect the accuracy of this calculation?

The accuracy of the calculation may be affected by external factors such as temperature and humidity, as well as internal factors such as the quality and condition of the components used in the circuit.

5. How can I apply this calculation in real-world scenarios?

This calculation can be applied in real-world scenarios such as designing and troubleshooting electronic circuits, determining the charging and discharging times of electronic devices, and analyzing the behavior of RC circuits in different applications.

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