Please answer the following question and show all work: Problem 1: For the circuit shown below,...

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Please answer the following question and show all work:

Problem 1: For the circuit shown below, use Kirchhoffs laws to calculate the currents 1, 12, 13. 40 1 40 20 V 2V 10V w OE OZ

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Answer 1

Answer #1

applying kirchoff's voltage law in left loop

so $-20 + 4I_{1}+ 2+3I_{2}+4I_{1}=0$

$8I_{1}+3I_{2}=18 -----(1)$

applying kirchoff's voltage law in right loop

$-10 + 4I_{3}+2+3I_{2}+2I_{3}= 0$

613 +312 = 8 - - - - (2

applying kirchoff's current law at upper node

so $I_{1}+I_{3}= I_{2}--------------(3)$

now put the value of $I_{2}$ from equation (3) in equation (1) & equation (2)

so the modified eqns

$3I_{1}+9I_{3}= 8-------(4)$

$11I_{1}+3I_{3}=1 8-------(5)$

by solving eqn(4) &eqn(5) we got

$I_{1}= 1.5333A$

$I_{3}= 0.378A$

put the value of $I_{3}$ and $I_{1}$ in eqn (3)

so we got $I_{2}= 1.9111A$

so

$I_{1}= 1.533A$

$I_{2}= 1.9111A$

$I_{3}= 0.377A$

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Answer 2

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