CKT: http://i44.tinypic.com/qxl0r5.jpg
Can somebody please help me with this, also if you answer it's imperative to me that you explain/go through the steps so I can see the error of my ways.
Q:
Use the Mesh Analysis to find the Norton Equivalent circuit for the circuit shown below from the viewpoint of the load resistor. Don't perform any source conversions.
My attempt: http://i44.tinypic.com/261lrwj.jpg
Please, I need help with this.
Can somebody please help me with this, also if you answer it's imperative to me that you explain/go through the steps so I can see the error of my ways.
Q:
Use the Mesh Analysis to find the Norton Equivalent circuit for the circuit shown below from the viewpoint of the load resistor. Don't perform any source conversions.
My attempt: http://i44.tinypic.com/261lrwj.jpg
Please, I need help with this.
-
You have 3 loops
V 5ma = (5ma)(5k) - I1(5k) where V 5ma is the voltage across the 5ma current source
-10 volt = -(5ma)(5k) +I1(18k) - I2(3k)
20 volt = -I1(3k) +(3k +RL)I2
To calculate the Norton source, we need the open voltage equivalent where RL --> ∞
I2 is 0
solve for I1, -10 volts = -(5ma)5k +18k(I1)
15 volts = 18k(I1), I1 = 0.833 mA
V 3k = I1(3k)= 2.5 volts
V open circuit = 20 +2.5 = 22.5 volts
We also need the short circuit current where RL =0
20 volts = -I1(3k) + I2(3k)
-I2(3k) = -20 -I1(3k)
-10 volts = -5ma(5k) +18k(I1) - 3k(I2)
15 volts = 18k(I1)- 3k(I2)
15 volts = 18k(I1) +(-I1(3k) -20)
15 volts = 15k(I1) -20
35/15k = I1, I1 = 2.33 mA
I2 the short circuit current is 20 volts = -(2.33 mA)(3k) +I2(3k)
27 volts/3k = 9 mA = I2
The short circuit current is 9 mA, the Norton current source is 9 mA
The equivalent parallel resistance R norton = 22.5/9mA= 2.5 K ohms
V 5ma = (5ma)(5k) - I1(5k) where V 5ma is the voltage across the 5ma current source
-10 volt = -(5ma)(5k) +I1(18k) - I2(3k)
20 volt = -I1(3k) +(3k +RL)I2
To calculate the Norton source, we need the open voltage equivalent where RL --> ∞
I2 is 0
solve for I1, -10 volts = -(5ma)5k +18k(I1)
15 volts = 18k(I1), I1 = 0.833 mA
V 3k = I1(3k)= 2.5 volts
V open circuit = 20 +2.5 = 22.5 volts
We also need the short circuit current where RL =0
20 volts = -I1(3k) + I2(3k)
-I2(3k) = -20 -I1(3k)
-10 volts = -5ma(5k) +18k(I1) - 3k(I2)
15 volts = 18k(I1)- 3k(I2)
15 volts = 18k(I1) +(-I1(3k) -20)
15 volts = 15k(I1) -20
35/15k = I1, I1 = 2.33 mA
I2 the short circuit current is 20 volts = -(2.33 mA)(3k) +I2(3k)
27 volts/3k = 9 mA = I2
The short circuit current is 9 mA, the Norton current source is 9 mA
The equivalent parallel resistance R norton = 22.5/9mA= 2.5 K ohms