Plusivo DM401B - Page 30

To use Kirchhoff's voltage law, we need to know some rules, for example, in if the loop passes
𝐿
1
the battery from - to + we write it in the equation (+3 V), but if the loop passes the battery from + to - we
write it in the equation (-3 V). Let us take 2.2 resistor as an example, if the loop passes the resistor in
𝑘Ω
the same direction with the current we write it , but if the loop passes the resistor in the
− 2. 2 𝑘Ω · 𝐼
1
( )
opposite direction with the current we write it ( ).
+ 2. 2 𝑘Ω · 𝐼
1
We get this equation from .
𝐿
1
Equation 1:
3 𝑉 − (𝐼
1
· 2. 2 𝑘Ω) − (𝐼
3
· 680 Ω) = 0 𝑉
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 to get I
3
,
𝐼
1
= 𝐼
2
+ 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)
29
Mastering the Art of Measurement (DM401B Smart Digital Multimeter) r.01 www.plusivo.com