Plusivo DMM - Page 30

We get this equation from .
𝐿
2
Equation 2:
(𝐼
3
· 680 Ω) + 3 𝑉 − (𝐼
2
· 47 Ω) = 0 𝑉
We get this equation from the node.
Equation 3:
𝐼
1
= 𝐼
2
+ 𝐼
3
Now, let us do some math to calculate , and .
𝐼
1
𝐼
2
𝐼
3
Equation 1:
3 𝑉 − (𝐼
1
· 2. 2 𝑘Ω) − (𝐼
3
· 680 Ω) = 0 𝑉
3 𝑉 − (𝐼
3
· 680 Ω) = 𝐼
1
· 2200 Ω
𝐼
1
=
3 𝑉
2200 Ω
−
𝐼
3
·680 Ω
2200 Ω
→ This becomes equation 4
𝐼
1
= 0. 001363 𝐴 − (𝐼
3
· 0. 3091)
Equation 2:
(𝐼
3
· 680 Ω) + 3 𝑉 − (𝐼
2
· 47 Ω) = 0 𝑉
𝐼
2
· 47 Ω = (𝐼
3
· 680 Ω) + 3 𝑉
𝐼
2
=
𝐼
3
· 680 Ω
47 Ω
+
3 𝑉
47 Ω
→ This becomes equation 5
𝐼
2
= (𝐼
3
· 14. 468) + 0. 0638 𝐴
Equation 4:
𝐼
1
= 0. 001363 𝐴 − (𝐼
3
· 0. 3091)
Equation 5:
𝐼
2
= (𝐼
3
· 14. 468) + 0. 0638 𝐴
From Equation 3: , we will use the derived I
1
and I
2
from previous calculation
𝐼
1
= 𝐼
2
+ 𝐼
3
to get I
3
, thus,
0. 001363 𝐴 − (𝐼
3
· 0. 3091) = (𝐼
3
· 14. 468) + 0. 0638 𝐴 + 𝐼
3
− 𝐼
3
· 0. 3091 = (𝐼
3
· 14. 468) + 0. 0638 𝐴 − 0. 001363 𝐴 + 𝐼
3
− 𝐼
3
· 0. 3091 = (𝐼
3
· 14. 468) + 0. 062437 + 𝐼
3
− 0. 062437 = (𝐼
3
· 0. 3091) + (𝐼
3
· 14. 468) + 𝐼
3
− 0. 062437 = 15. 7771 · 𝐼
3
𝐼
3
= − 0. 003957 𝐴
Equation 4:
𝐼
1
= 0. 001363 𝐴 − (𝐼
3
· 0. 3091)
𝐼
1
= 0. 001363 𝐴 − (− 0. 003957 𝐴 · 0. 3091)
𝐼
1
= 0. 001363 𝐴 + 0. 001223 𝐴
𝐼
1
= 0. 002586 𝐴
Equation 5:
𝐼
2
= (𝐼
3
· 14. 468) + 0. 0638 𝐴
𝐼
2
= (− 0. 003957 𝐴 · 14. 468) + 0. 0638 𝐴
𝐼
2
= − 0. 05725 𝐴 + 0. 0638 𝐴
𝐼
2
= 0. 00655 𝐴
29
Mastering the Art of Measurement (Digital Multimeter) r.01 www.plusivo.com