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Finding current using Kirchhoff's Rules...?
Using Kirchhoff's rules, calculate the current in R1 with the directions indicated in the figure below.
IMAGE: https://spock.physast.uga.edu/res/brookscole/serwa...
Assume that R1 = 4.00 kohm, R2 = 6.00 kohm, R3 = 8.00 kohm, E1 = 75.0 V, E2 = 60.0 V and E3= 85.0 V.
Calculate the current in R 1, R2 and R3...
Find the magnitude of the potential difference between points c and f.
2 Answers
- godzyxLv 68 years agoFavorite Answer
Both links are not working.
Is this your circuit?
http://www.flickr.com/photos/94621593@N04/with/861...
KCL at junction c.
1. I2 = I1 + I3
KVL 1st loop.
2. -E2 + I2 R2 + I1 R1 + E1 = 0
I2 R2 + I1 R1 = E2 - E1
6kΩ I2 + 4kΩ I1 = 60V - 75V
2a. 6kΩ I2 + 4kΩ I1 = -15V
KVL 2nd loop.
3. -I2 R2 + E2 - I3 R3 - E3 = 0
-I2 R2 - I3 R3 = E3 - E2
-6kΩ I2 - 8kΩ I3 = 85V - 60V
3a. -6kΩ I2 - 8kΩ I3 = 25V
Solve 3a for I3, solve 2a for I1 and substitute into 1 and solve for I2.
-6kΩ I2 - 8kΩ I3 = 25V
-8kΩ I3 = 25V + 6kΩ I2
I3 = (10V + 6kΩ I2) / -8kΩ = -3.125mA - 0.75 I2
6kΩ I2 + 4kΩ I1 = -15V
4kΩ I1 = -15V - 6kΩ I2
I1 = (-15V - 6kΩ I2) / 4kΩ = -3.75mA - 1.5 I2
I2 = I1 + I3
I2 = (-3.75mA - 1.5 I2) + (-3.125mA - 0.75 I2)
I2 + 1.5 I2 + 0.75 I2 = -3.75mA - 3.125mA
3.25 I2 = -6.875mA
I2 = -2.115mA
Negative current means assumed direction is incorrect. Substitute this into 2a and 3a and solve for other currents.
6kΩ I2 + 4kΩ I1 = -15V
6kΩ (-2.115mA) + 4kΩ I1 = -15V
I1 = -0.578mA
-6kΩ I2 - 8kΩ I3 = 25V
-6kΩ (-2.115mA) - 8kΩ I3 = 25V
I3 = -1.538mA
All three currents actually flow in the opposite directions, but as shown on drawing are negative.
So V_cf = E2 - I2 R2 = +60V - (-2.115mA) * 6kΩ = 72.7V