Answer:
Answer is explained in the explanation section below.
Explanation:
Note: This question is incomplete and lacks the necessary diagram of the circuits to solve for this question. However, I have found similar question on the internet and dragged the diagrams out of it. I have attached the diagrams of the circuits for your ease. It has two circuits to be solved. Attachment 1 refers to first circuit and Attachment 2 refers to second circuit.
Solution:
We are asked to find the potential difference and current through each resistor.
So,
Calculations for Circuit 1: Please refer to Attachment 1
First we need to find the Resistance:
Req = [tex]\frac{9 . 6}{9+6} +3[/tex]
R = 6.6 Ohm
Now, we know that:
V = IR
So,
I = V/R
V = 12 V
I = 12 V/ 6.6 ohm
I = 1.82 Amperes.
Now,
The Potential Difference through 3 ohm resistor:
P.D = [tex]V_{3}[/tex] = 1.82 x 3
[tex]V_{3}[/tex] = 5.45 V
Now,
The Potential Difference through 6 ohm and 9 ohm resistor:
[tex]V_{6/9}[/tex] = 12V - 5.45V
[tex]V_{6/9}[/tex] = 6.545V
Now,
The current through 6 ohm is:
[tex]I_{6}[/tex] = [tex]\frac{6.545}{6}[/tex]
[tex]I_{6}[/tex] = 1.09 A
Now,
The Current through 9 ohm is:
[tex]I_{9}[/tex] = [tex]\frac{6.545}{9}[/tex]
[tex]I_{9}[/tex] = 0.72 A
Similarly,
Calculations for Circuit 2: Please refer to attachment 2:
Req = [tex]\frac{(30+50).90}{90+(30+50)} +20[/tex]
Req = 62.35 ohm
I = V/R
I = 12 V/ 62.35ohm
I = 0.192 Amperes.
Now,
The The Potential Difference through 20 ohm resistor:
[tex]V_{20}[/tex] = 20 x 0.192
[tex]V_{20}[/tex] = 3.849 V
Now,
The The Potential Difference through 90 ohm resistor:
[tex]V_{90/(30+50)}[/tex] = 12 - 3.849
[tex]V_{90/(30+50)}[/tex] = 8.150
Now,
The Current through 90 ohm is:
[tex]I_{90}[/tex] = 8.1509/90
[tex]I_{90}[/tex] = 0.0905 Amperes
Now,
The Current through 30 and 50 ohm is:
[tex]I_{30/50}[/tex] = 0.192 - 0.0905
[tex]I_{30/50}[/tex] = 0.101 A
Now,
The Potential Difference through 50 ohm resistor:
[tex]V_{50}[/tex] = 50 x 0.101
[tex]V_{50}[/tex] = 5.094 V
The Potential Difference through 30 ohm resistor:
[tex]V_{30}[/tex] = 30 x 0.101
[tex]V_{30}[/tex] = 3.0566 V
