2.9 Summary

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2.9 Summary

1. A resistor is a passi ve element in which the v oltage v across it is directly proportional to the current i through it. That is, a resistor is a device that obeys Ohm’s law,

v = iR

where R is the resistance of the resistor.

• 2. A short circuit is a resistor (a perfectly , conducting wire) with zero resistance (R = 0). An open circuit is a resistor with infinite resistance (R = ∞).
• 3. The conductance G of a resistor is the reciprocal of its resistance:

$$G = \frac{1}{R}$$

4. A branch is a single tw o-terminal element in an electric circuit. A node is the point of connection between tw o or more branches. A loop is a closed path in a circuit. The number of branches b, the number of nodes n, and the number of independent loops l in a network are related as

$$b = l + n - 1$$

• 5. Kirchhoff’s current law (KCL) states that the currents at an y node algebraically sum to zero. In other w ords, the sum of the currents entering a node equals the sum of currents leaving the node.
• 6. Kirchhoff’s v oltage la w (KVL) states that the v oltages around a closed path algebraically sum to zero. In other w ords, the sum of voltage rises equals the sum of voltage drops.
• 7. Two elements are in series when the y are connected sequentially , end to end. When elements are in series, the same current flows through them (i¹ = i2). They are in parallel if the y are connected to the same two nodes. Elements in parallel always have the same voltage across them (v¹ = v2).
• 8. When two resistors R1 (=1/G1) and R2 (=1/G2) are in series, their equivalent resistance Req and equivalent conductance Geq are

$$R_{\text{eq}} = R_1 + R_2,$$

$G_{\text{eq}} = \frac{G_1 G_2}{G_1 + G_2}$

9. When two resistors R1 (=1/G1) and R2 (=1/G2) are in parallel, their equivalent resistance Req and equivalent conductance Geq are

$$R_{\text{eq}} = \frac{R_1 R_2}{R_1 + R_2}, \qquad G_{\text{eq}} = G_1 + G_2$$

Practice Problem 2.17

10. The voltage division principle for two resistors in series is

$$v_1 = \frac{R_1}{R_1 + R_2} v$$

, $v_2 = \frac{R_2}{R_1 + R_2} v$

11. The current division principle for two resistors in parallel is

$$i_1 = \frac{R_2}{R_1 + R_2} i$$

, $i_2 = \frac{R_1}{R_1 + R_2} i$

12. The formulas for a delta-to-wye transformation are

$$R_1 = \frac{R_b R_c}{R_a + R_b + R_c}, \qquad R_2 = \frac{R_c R_a}{R_a + R_b + R_c}$$ $$R_3 = \frac{R_a R_b}{R_a + R_b + R_c}$$

13. The formulas for a wye-to-delta transformation are

The formulas for a wye-to-delta transformation are
\n

$$R_a = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_1}, \qquad R_b = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_2}$$

\n

$$R_c = \frac{R_1 R_2 + R_2 R_3 + R_3 R_1}{R_3}$$

14. The basic laws covered in this chapter can be applied to the problems of electrical lighting and design of dc meters.

Review Questions

2.1		The reciprocal of resistance is:

(a) voltage	(b) current
(c) conductance	(d) coulombs

2.2 An electric heater draws 10 A from a 120-V line. The resistance of the heater is:

(a) 1200 Ω	(b) 120 Ω
(c) 12 Ω	(d) 1.2 Ω

2.3 The voltage drop across a 1.5-kW toaster that draws 12 A of current is:

(a) 18 kV	(b) 125 V
(c) 120 V	(d) 10.42 V

2.4 The maximum current that a 2W, 80 kΩ resistor can safely conduct is:

(a) 160 kA	(b) 40 kA
(c) 5 mA	(d) 25 μA

2.5 A network has 12 branches and 8 independent loops. How many nodes are there in the network?

(a) 19 (b) 17 (c) 5 (d) 4

2.6 The current I in the circuit of Fig. 2.63 is:

(a) −0.8 A	(b) −0.2 A
(c) 0.2 A	(d) 0.8 A

Figure 2.63

For Review Question 2.6.

2.7 The current Io of Fig. 2.64 is:

(a)

$$-4$$

A (b) $-2$ A (c) $4$ A (d) $16$ A

Problems 65

2.8 In the circuit in Fig. 2.65, V is: (a) 30 V (b) 14 V (c) 10 V (d) 6 V