# Calculating Current in a Single-Loop Circuit with Resistor and Capacitor

• reising1
In summary: That's correct. In summary, the conversation discusses a battery connected to a circuit with two resistors and a capacitor. After the battery is removed, the circuit contains only two resistors and a capacitor. The question is about the current going through one of the resistors. The conversation also includes a solution attempt using equations for an RL circuit, but there are several errors and suggestions to rethink the strategy.
reising1

## Homework Statement

There is a Battery connected to a single loop circuit containing two resistors, R1 and R2, and one capacitor L.

After a long time, the battery is removed, so there is a single loop circuit with just two resistors and a capacitor.

What is the current going through R1?

## The Attempt at a Solution

This is what I thought:

So, the EMF is removed. Thus, using a loop rule, we have the formula:

0 = IR + L(di/dt) where R is R1+R2

Integrating, we have

0 = (1/2)(I^2)(R) + (L)(I)

Dividing everything by I, we have

0 = (1/2)(I)(R) + L

Thus, I = (2L) / R

However, this is incorrect.

Any ideas?

Thanks!

There are a few problems here. You call this an RL circuit, and you use the equations for an RL circuit, but you say it contains a capacitor instead of an inductor. I assume you are just using the wrong word.

The second problem is here:
reising1 said:
0 = IR + L(di/dt) where R is R1+R2

Integrating, we have

0 = (1/2)(I^2)(R) + (L)(I)
Are you sure you did that correctly? What variable are you integrating with respect to?

Oh, wait. That is wrong.

With respect to I, you get:

R + LI = 0

So I = -R/L?

Deriving with respect to I. Sorry.

This is still not right because you differentiated one term and integrated the other.

You might want to rethink the whole strategy of trying to take an integral or a derivative.
You have both I and dI/dt in this equation. What kind of equation does that make it?

What do you mean?

d/di(RI) = R
d/di(L(di/dt)) = LI

differential equation

reising1 said:
What do you mean?

d/di(RI) = R
d/di(L(di/dt)) = LI

Taking a derivative of a derivative doesn't make the derivative do away.

reising1 said:
differential equation

Yes!

## What is a single-loop circuit?

A single-loop circuit is a circuit that has only one path for the electric current to flow. It typically consists of a power source, a resistor, and a capacitor connected in a loop.

## How do I calculate the current in a single-loop circuit?

To calculate the current in a single-loop circuit, you can use Ohm's Law (I=V/R) to calculate the current through the resistor, and use the equation I=C*dV/dt to calculate the current through the capacitor. Then, add these two currents together to get the total current in the circuit.

## What is the role of a resistor in a single-loop circuit?

A resistor is used to limit the flow of electric current in a circuit. It helps to control the amount of current that flows through the circuit and prevents damage to components.

## How does a capacitor affect the current in a single-loop circuit?

A capacitor stores electric charge and can affect the current in a single-loop circuit by either allowing or blocking the flow of current, depending on the frequency and voltage of the current.

## Can I use the same formula to calculate the current in any single-loop circuit?

Yes, the same formula can be used to calculate the current in any single-loop circuit, as long as the circuit consists of a power source, a resistor, and a capacitor connected in a loop.

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