32a is redrawn in fig 32b where we now add i1 i2 and

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Unformatted text preview: , the circuit in Fig. 3.2(a) is redrawn in Fig. 3.2(b), where we now add i1 , i2 , and i3 as the currents through resistors R1 , R2 , and R3 , respectively. At node 1, applying KCL gives I1 = I2 + i1 + i2 77 The number of nonreference nodes is equal to the number of independent equations that we will derive. (a) Figure 3.1 Common symbols for indicating a reference node. I2 (3.1) At node 2, I2 + i2 = i3 (c) (b) R2 1 2 (3.2) We now apply Ohm’s law to express the unknown currents i1 , i2 , and i3 in terms of node voltages. The key idea to bear in mind is that, since resistance is a passive element, by the passive sign convention, current must always flow from a higher potential to a lower potential. I1 + v1 − + v2 − R1 R3 0 (a) Current flows from a higher potential to a lower potential in a resistor. I2 We can express this principle as i= vhigher − vlower R v1 i2 R2 i2 v2 i1 (3.3) I1 i3 R1 R3 Note that this principle is in agreement with the way we defined resistance in Chapter 2 (see...
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