- #1

jisbon

- 476

- 30

- Homework Statement
- -

- Relevant Equations
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Hi all,

Checking my answers here as it doesn't seem to match with the answers given to me. Would appreciate if anyone could point out the mistakes I made.

First I will compute Rth. Offing all independent sources, applying a known voltage across R (in this case 1v) and using mesh analysis,

2i1+0 (since i =0) + 3i1+5(i1-i2) = 0

10i1=5i2

5i1=2.5i2 -- Equation 1

2nd Loop:

5(i2-i1)+1 =0

Combing this with equation 1,

5i2 - 2.5i2 +1 =0

i2 = -0.4A

Hence Rth = 1/0.4 = 2.5 ohms.

Note: For Rth, the answer stated was 1.92ohms using nodal analysis.

Now to find Vth, I will just use normal mesh analysis for the normal circuit:

Mesh 1:

=-10+i1+2(i1-i2)=0 --> -10+3i1-2i2=0 --> **2i2 = 10+3i1**

Mesh 2:

2(i2-i1) - 2i1 +3i2+5(i2-i3) =0 --> **i1 = (-10i2+5i3)/4**

Mesh 3:

5(i3-i2)+Vr= 0 --> Vr= 5i2-5i3

Around whole loop:

=-10+i1-2i1+3i2+Vr=0 --> Using Mesh 3 equation, **i1=8i2-5i3-10**

Solving these 3 equations, i3 = 0.5A, i2 = 1.25A

Hence Vrth = 5( 1.25- 0.5) = 3.75V

Pmax =(Vrth^2)/4Rth = 1.40W?

Thanks.

Checking my answers here as it doesn't seem to match with the answers given to me. Would appreciate if anyone could point out the mistakes I made.

First I will compute Rth. Offing all independent sources, applying a known voltage across R (in this case 1v) and using mesh analysis,

2i1+0 (since i =0) + 3i1+5(i1-i2) = 0

10i1=5i2

5i1=2.5i2 -- Equation 1

2nd Loop:

5(i2-i1)+1 =0

Combing this with equation 1,

5i2 - 2.5i2 +1 =0

i2 = -0.4A

Hence Rth = 1/0.4 = 2.5 ohms.

Note: For Rth, the answer stated was 1.92ohms using nodal analysis.

Now to find Vth, I will just use normal mesh analysis for the normal circuit:

Mesh 1:

=-10+i1+2(i1-i2)=0 --> -10+3i1-2i2=0 --> **2i2 = 10+3i1**

Mesh 2:

2(i2-i1) - 2i1 +3i2+5(i2-i3) =0 --> **i1 = (-10i2+5i3)/4**

Mesh 3:

5(i3-i2)+Vr= 0 --> Vr= 5i2-5i3

Around whole loop:

=-10+i1-2i1+3i2+Vr=0 --> Using Mesh 3 equation, **i1=8i2-5i3-10**

Solving these 3 equations, i3 = 0.5A, i2 = 1.25A

Hence Vrth = 5( 1.25- 0.5) = 3.75V

Pmax =(Vrth^2)/4Rth = 1.40W?

Thanks.