- #1

marchcha

- 15

- 1

## Homework Statement

A circuit is constructed with four resistors, one capacitor, one battery and a switch as shown. The values for the resistors are: R1 = R2 = 41 Ω, R3 = 68 Ω and R4 = 154 Ω. The capacitance is C = 49 μF and the battery voltage is V = 12 V. The positive terminal of the battery is indicated with a + sign.

What is Q(∞), the charge on the capacitor after the switch has been closed for a very long time?

## Homework Equations

Kirchhoff's Laws

## The Attempt at a Solution

I attempted to find Q(inf) by setting up kirchhoffs voltage and loop equations as shown:

1. I1 = I4

2. 14 = I2 + I3

3. V - I1R1 - I3R3 - I4R4 = 0

4. V - I1R1 - I2R2 - (Q/C) - I4R4 = 0

I used the equalities in equation 1 to solve equation 3 in terms of I3. I then used I3 from equation 3 and plugged it into equation 2 to get an equation for I2. I then plugged in what I got for I2 into equation 4 as well as plugging in I4 for I1. The final equation I got for the value of Q is: Q = C(V - I4R4 - (I4 - (V - I4(R1 + R4))/R3) * R2 - I4R4). I had already found the value for I4 in a previous problem using V = IR when the switch is closed for a very long time. I4's value is 0.54A.

Thank you so much in advance!