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Unformatted text preview: meshes 1 and
2. Although a mesh current may be assigned to each mesh in an arbitrary direction, it is conventional to assume that each mesh current ﬂows
As the second step, we apply KVL to each mesh. Applying KVL
to mesh 1, we obtain The direction of the mesh current is arbitrary—
(clockwise or counterclockwise)—and does not
affect the validity of the solution. −V1 + R1 i1 + R3 (i1 − i2 ) = 0
(R1 + R3 )i1 − R3 i2 = V1 (3.13) For mesh 2, applying KVL gives
R2 i2 + V2 + R3 (i2 − i1 ) = 0
−R3 i1 + (R2 + R3 )i2 = −V2 (3.14) Note in Eq. (3.13) that the coefﬁcient of i1 is the sum of the resistances in
the ﬁrst mesh, while the coefﬁcient of i2 is the negative of the resistance
common to meshes 1 and 2. Now observe that the same is true in Eq.
(3.14). This can serve as a shortcut way of writing the mesh equations.
We will exploit this idea in Section 3.6.
The third step is to solve for the mesh currents. Putting Eqs. (3.13)
and (3.14) in matrix form yields R1 + R3
R2 + R 3 i1
−V2 The shortcut way will not apply...
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- Spring '12