Need help with especially the last 2 questions The emf\'s and the resistors in t
ID: 2260183 • Letter: N
Question
Need help with especially the last 2 questions
The emf's and the resistors in the two-loop circuit are given as indicated in the figure. The arrow directions in the circuit set up the sign convention. The current values can be positive or negative. Find I3 in terms of I1 and I2 by Kirchhoff's Rule I. Write down explicitly Kirchhoff's Rule II for the left loop, ONLY in terms of I1 and I2 (no symbol I3) Write down explicitly Kirchhoff's Rule II for the left loop, ONLY in terms of I1 and I2. (no symbol I3) Determine values of currents I1, I2, and I3. Find the voltage difference Va - Vb across points a and b.Explanation / Answer
iv)
10 - 8 - 3 i3 + 4 i1 = 0
==> 3 i3 = 10 - 8 + 4 i1
==> 3 i3 = 2 + 4 i1
==> i3 = 2/3 + 4/3 i1
==> i3 = 0.6667 + 1.333 i1
17 - 8 - 3 i3 + i2 = 0 ;
==> i2 = -17 + 8 + 3 i3
==> i2 = -9 + 3 i3
==> i2 = -9 + 3 (0.6667 + 1.333 i1)
==> i2 = -9 + 2 + 4 i1
==> i2 = -7 + 4 i1
i1 + i2 = i3
==> i1 + (-7 + 4 i1) = 0.6667 + 1.333 i1
==> i1 + 4 i1 - 1.333 i1 = 0.6667 + 7
==> i1 = 2.09 A
i2 = -7 + 4 i1 = -7 + 4*2.09 = 1.36 A
i3 = 0.6667 + 1.333 i1 = 0.6667 + 1.333*2.09 = 3.45 A
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therefore:
i1 = 2.09 A
i2 = 1.36 A
i3 = 3.45 A
v)
Va + 3 i3 + 8 = Vb
==> Va - Vb = -3i3 - 8 = -3*3.45 - 8 = -18.4 V