# RC Circuit , Calculate Time Constant

• ParoXsitiC
In summary, the conversation is about finding the time constant of a complex circuit using junction and loop rules. The speaker is confused and trying to figure out how to calculate it for a complex circuit. The teacher provides the equation and mentions that [foo] would be the time constant and [bar] would be the equivalent resistance to the battery. The conversation ends with the need to simplify the equation and solve for [foo].
ParoXsitiC

## Homework Statement

Given this diagram:

Picture mirror: http://i.minus.com/1331507225/3XjEXOAlTaoJBoBuQFoJiQ/itFBvAiitDZQc.png

With S1 switch closed and S2 switch left open, I am trying to find the time constant

## Homework Equations

I know τ = RC for a basic circuit, but how would you calculate it for a complex circuit? Is R the equivalent resistance to the battery?

Q=VC
V=IR

i = dq/dt
dq/dt + Q/τ - emf / R = 0

## The Attempt at a Solution

I1 = I2 + I3
-emf + I1R1 + Q/C + I2R2 = 0
=emf + I1R1 + I3R3 + I3R4 = 0

At this point the teacher says I2 = dq/dt and we need to get rid of I1 so we can put something next to the C in Q/C.

I use I1 = I2+I3 in junction rule and put it into loop rule #2, getting:

-emf + (I2 + I3)R1 + I3R3 + I3R4 = 0
I2R1 + I3(R1+R3+R4) = emf
I3 = (emf - I2R1) / (R1+R3+R3)

Then I put I3 in for the I1 eq.

I1 = I2 + (emf - I2R1) / (R1+R3+R3)

At this point it's so messy and confusing I think I am doing it all wrong.

The baseline she is giving us is that

dq/dt + Q/[foo] - emf/[bar] = 0

where [foo] would be the time constant. In a simple circuit she gives [foo] = RC and [bar] = R

Last edited:
I do not see any diagram... ehild

ehild said:
I do not see any diagram...

ehild

Weird, it's possible minus.com isn't showing up for you. I will upload it

## 1. What is an RC circuit?

An RC circuit is an electrical circuit that consists of a resistor (R) and a capacitor (C) connected in series or parallel. It is used to control the flow of current and store electrical energy.

## 2. How do you calculate the time constant of an RC circuit?

The time constant (τ) of an RC circuit can be calculated by multiplying the resistance (R) in ohms by the capacitance (C) in Farads. The formula is τ = R x C.

## 3. What is the significance of the time constant in an RC circuit?

The time constant represents the time it takes for the capacitor to charge or discharge to 63.2% of its maximum voltage. It is also used to determine the rate of change of voltage or current in the circuit.

## 4. How does the time constant affect the behavior of an RC circuit?

The time constant determines the speed at which the capacitor charges or discharges, which affects the behavior of the circuit. A shorter time constant results in a faster charging or discharging process, while a longer time constant results in a slower process.

## 5. Can the time constant be changed in an RC circuit?

Yes, the time constant can be changed by altering the resistance or capacitance in the circuit. Increasing the resistance or capacitance will result in a longer time constant, while decreasing them will result in a shorter time constant.

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