Solved: Calculating Capacitor Charge in Circuits with 115V, 30R & Switch Closed

In summary, the conversation pertains to a circuit with a DC source, resistors, and a capacitor. The switch has been closed for a long time and the goal is to find the charge on the capacitor and the time it takes for it to lose 10% of its charge. The equations used involve the loop laws and there are 3 equations and 4 variables, so further analysis is needed.
  • #1
parkskier
7
0

Homework Statement


V = 115 V, R = 30 , and the switch has been closed for a very long time.

Diagram:
p31-77alt.gif


Homework Equations



Q=CV
V=IR

The Attempt at a Solution



I thought it would be a good idea to use the Loop Laws I get the following equations (If Loop 1 is the larger loop with the battery, and Loop 2 is the smaller one):

L1: 115-60I1-30I3=0
L2: 30I3-10I2-Q/2.0microF=0
I1=I2+I3

Where I1 is the current through the battery and 60 ohm resistor; I2 is the current through the 10 ohm resistor and capacitor; I3 is the current through the middle resistor.

However, with this there are 3 equations and 4 variables, so something is wrong, or I'm approaching it wrong. Thanks for any help.
 
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  • #2
First of all you should note that if the switch has been closed for an infinite period of time and you're using a DC source, then the current flowing through the right loop containing the 10 ohm resistor and the capacitor is 0A. You need to solve it for the case where t<0 and t>0 separately.
 
  • #3
Sorry, I forgot one part of the problem. I'm supposed to solve for what the charge on the capacitor is after the switch has been closed for a very long time...and then solve for how much time it takes for the capacitor to lose 10% of it's charge when the switch is opened.
 

Related to Solved: Calculating Capacitor Charge in Circuits with 115V, 30R & Switch Closed

What is a capacitor?

A capacitor is an electronic component that is designed to store electrical charge. It consists of two conductive plates separated by an insulating material, known as a dielectric.

How do you calculate capacitor charge in circuits?

The formula for calculating capacitor charge in a circuit is Q = CV, where Q is the charge, C is the capacitance, and V is the voltage. In this case, the voltage is 115V and the capacitance is 30R. Therefore, the charge would be 3,450 coulombs.

What is the significance of the switch being closed?

When the switch is closed in a circuit, it allows current to flow through the circuit and charge the capacitor. This results in the capacitor reaching its maximum charge, as determined by the voltage and capacitance of the circuit.

Why is it important to calculate capacitor charge in circuits?

Calculating capacitor charge in circuits is important because it helps in understanding the behavior of the circuit and determining the amount of energy stored in the capacitor. This information is crucial in designing and troubleshooting electronic circuits.

Are there any safety precautions to consider when working with circuits and capacitors?

Yes, it is important to take proper safety precautions when working with circuits and capacitors. Always make sure the circuit is disconnected from any power source before handling capacitors. Additionally, capacitors can hold a charge even after the power is turned off, so it is important to discharge them using a resistor before handling. It is also recommended to wear protective gear, such as gloves and safety glasses, when working with circuits and capacitors.

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