Problems

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Problems

Section 2.2 Ohm’s Law

2.1 Design a problem, complete with a solution, to help students to better understand Ohm’s law. Use at least two resistors and one voltage source. Hint, you could use both resistors at once or one at a time, it is up to you. Be creative.

• 2.10 In the circuit of Fig. 2.67, a decrease in R3 leads to a decrease of, select all that apply:
  • (a) current through R³
  • (b) voltage across R³
  • (c) voltage across R¹
  • (d) power dissipated in R²
  • (e) none of the above

Figure 2.67 For Review Question 2.10.

Answers: 2.1c, 2.2c, 2.3b, 2.4c, 2.5c, 2.6b, 2.7a, 2.8d, 2.9d, 2.10b, d.

• 2.2 Find the hot resistance of a light bulb rated 60 W, 120 V.

• 2.3 A bar of silicon is 4 cm long with a circular cross sec tion. If the resistance of the bar is 240 Ω at room tem perature, what is the cross-sectional radius of the bar?

• 2.4 (a) Calculate current i in Fig. 2.68 when the switch is in position 1.

  • (b) Find the current when the switch is in position 2.

Figure 2.68

For Prob. 2.4.

Section 2.3 Nodes, Branches, and Loops

2.5 For the network graph in Fig. 2.69, find the number of nodes, branches, and loops.

Figure 2.69 For Prob. 2.5.

2.6 In the network graph shown in Fig. 2.70, determine the number of branches and nodes.

2.7 Determine the number of branches and nodes in the circuit of Fig. 2.71.

Figure 2.71 For Prob. 2.7.

Section 2.4 Kirchhoff’s Laws

2.8 Design a problem, complete with a solution, to help

other students better understand Kirchhoff’s Current Law. Design the problem by specifying values of ia, ib, and ic, shown in Fig. 2.72, and asking them to solve for values of i1, i2, and i3. Be careful to specify realistic currents.

Figure 2.72

For Prob. 2.8.

2.9 Find i1, i2, and i3 in Fig. 2.73.

Figure 2.73 For Prob. 2.9.

2.10 Determine i1 and i2 in the circuit of Fig. 2.74.

Figure 2.74 For Prob. 2.10.

2.11 In the circuit of Fig. 2.75, calculate V1 and V2.

For Prob. 2.11.

2.12 In the circuit in Fig. 2.76, obtain v1, v2, and v3.

For Prob. 2.12.

2.13 For the circuit in Fig. 2.77, use KCL to find the branch currents I1 to I4.

Figure 2.77 For Prob. 2.13.

2.14 Given the circuit in Fig. 2.78, use KVL to find the branch voltages V1 to V4.

Figure 2.78 For Prob. 2.14.

2.15 Calculate v and ix in the circuit of Fig. 2.79.

For Prob. 2.15.

2.16 Determine Vo in the circuit in Fig. 2.80.

2.17 Obtain v1 through v3 in the circuit of Fig. 2.81.

2.18 Find I and V in the circuit of Fig. 2.82.

Figure 2.82 For Prob. 2.18.

For Prob. 2.19.

2.19 From the circuit in Fig. 2.83, find I, the power dissipated by the resistor, and the power supplied by each source.

2.20 Determine io in the circuit of Fig. 2.84.

• For Prob. 2.20.
• 2.21 Find Vx in the circuit of Fig. 2.85.

2.22 Find Vo in the circuit in Fig. 2.86 and the power absorbed by the dependent source.

• 2.23 In the circuit shown in Fig. 2.87, determine Vx and
  • the power absorbed by the 60-Ω resistor.

2.24 For the circuit in Fig. 2.88, find Vo / Vs in terms of α, R1, R2, R3, and R4. If R¹ = R² = R³ = R4, what value of α will produce |Vo / Vs| =10?

Figure 2.88 For Prob. 2.24.

2.25 For the network in Fig. 2.89, find the current, voltage, and power associated with the 20-kΩ resistor.

Sections 2.5 and 2.6 Series and Parallel Resistors

2.26 For the circuit in Fig. 2.90, io = 3 A. Calculate ix and the total power absorbed by the entire circuit.

Figure 2.90 For Prob. 2.26.

2.27 Calculate Io in the circuit of Fig. 2.91.

Figure 2.91 For Prob. 2.27.

Problems 69

2.28 Design a problem, using Fig. 2.92, to help other students better understand series and parallel circuits.

Figure 2.92 For Prob. 2.28.

2.29 All resistors (R) in Fig. 2.93 are 10 Ω each. Find Req.

Figure 2.93 For Prob. 2.29.

2.30 Find Req for the circuit in Fig. 2.94.

2.31 For the circuit in Fig. 2.95, determine i1 to i5.

For Prob. 2.31.

2.32 Find i1 through i4 in the circuit in Fig. 2.96.

Figure 2.96

For Prob. 2.32.

2.33 Obtain v and i in the circuit of Fig. 2.97.

Figure 2.97

For Prob. 2.33.

2.34 Using series/parallel resistance combination, find the equivalent resistance seen by the source in the circuit of Fig. 2.98. Find the overall absorbed power by the resistor network.

Figure 2.98 For Prob. 2.34.

2.35 Calculate Vo and Io in the circuit of Fig. 2.99.

2.36 Find i and Vo in the circuit of Fig. 2.100.

2.37 Given the circuit in Fig. 2.101 and that the resistance, Req, looking into the circuit from the left is equal to 100 Ω, determine the value of R1.

2.39 Evaluate Req looking into each set of terminals for each of the circuits shown in Fig. 2.103.

2.40 For the ladder network in Fig. 2.104, find I and Req.

Figure 2.104

For Prob. 2.40.

Figure 2.105

For Prob. 2.41.

2.42 Reduce each of the circuits in Fig. 2.106 to a single resistor at terminals a-b.

For Prob. 2.37.

2.38 Find Req and io in the circuit of Fig. 2.102.

Figure 2.106

For Prob. 2.42.

2.43 Calculate the equivalent resistance Rab at terminals a-b for each of the circuits in Fig. 2.107.

2.45 Find the equivalent resistance at terminals a-b of each circuit in Fig. 2.109.

Figure 2.109 For Prob. 2.45.

2.44 For the circuits in Fig. 2.108, obtain the equivalent resistance at terminals a-b.

Figure 2.108 For Prob. 2.44.

2.46 Find I in the circuit of Fig. 2.110.

For Prob. 2.46.

2.47 Find the equivalent resistance Rab in the circuit of Fig. 2.111.

Section 2.7 Wye-Delta Transformations

2.48 Convert the circuits in Fig. 2.112 from Y to Δ.

2.50 Design a problem to help other students better understand wye-delta transformations using Fig. 2.114.

Figure 2.114

For Prob. 2.50.

2.51 Obtain the equivalent resistance at the terminals a-b for each of the circuits in Fig. 2.115.

Figure 2.115 For Prob. 2.51.

2.52 For the circuit shown in Fig. 2.116, find the equivalent resistance. All resistors are 3Ω. *

* An asterisk indicates a challenging problem.

Problems 73

2.53 Obtain the equivalent resistance R 2.56 Determine V in the circuit of Fig. 2.120. ab in each of the circuits of Fig. 2.117. In (b), all resistors have a value of 30 Ω. *

2.54 Consider the circuit in Fig. 2.118. Find the equivalent resistance at terminals: (a) a-b, (b) c-d.

2.55 Calculate Io in the circuit of Fig. 2.119.

For Prob. 2.55.

For Prob. 2.56.

2.57 Find Req * and I in the circuit of Fig. 2.121.

Figure 2.121

For Prob. 2.57.

Section 2.8 Applications

2.58 The 150 W light bulb in Fig. 2.122 is rated at 110 volts. Calculate the value of Vs to make the light bulb operate at its rated conditions.

2.59 An enterprising young man travels to Europe carrying three light bulbs he had purchased in North America. The light bulbs he has are a 100-W light bulb, a 60-W light bulb, and a 40-W light bulb. Each light bulb is rated at 110 V. He wishes to connect these to a 220-V system that is found in Europe. For reasons we are not sure of, he connects the 40-W

light bulb in series with a parallel combination of the 60-W light bulb and the 100-W light bulb as shown in Fig. 2.123. How much power is actually being delivered to each light bulb? What does he see when he first turns on the light bulbs?

Is there a better way to connect these light bulbs in order to have them work more effectively?

• 2.60 If the three bulbs of Prob. 2.59 are connected in parallel to the 120-V source, calculate the current through each bulb.
• 2.61 As a design engineer, you are asked to design a
• lighting system consisting of a 70-W power supply and two light bulbs as shown in Fig. 2.124. You must select the two bulbs from the following three available bulbs.

R¹ = 80 Ω, cost = $0.60 (standard size) R² = 90 Ω, cost = $0.90 (standard size) R³ = 100 Ω, cost = $0.75 (nonstandard size)

The system should be designed for minimum cost such that I lies within the range I = 1.2 A ± 5 percent.

For Prob. 2.61.

2.62 A three-wire system supplies two loads A and B as shown in Fig. 2.125. Load A consists of a motor drawing a current of 8 A, while load B is a PC drawing 2 A. Assuming 10 h/day of use for 365 days and 6 cents/kWh, calculate the annual energy cost of the system.

Figure 2.125

• 2.63 If an ammeter with an internal resistance of 100 Ω and a current capacity of 2 mA is to measure 5 A, determine the value of the resistance needed. Calculate the power dissipated in the shunt resistor.
• 2.64 The potentiometer (adjustable resistor) Rx in Fig. 2.126 is to be designed to adjust current ix from 10 mA to 1 A. Calculate the values of R and Rx to achieve this.

Figure 2.126 For Prob. 2.64.

• 2.65 Design a circuit that uses a d’Arsonval meter (with an internal resistance of 2 kΩ that requires a current of 5 mA to cause the meter to deflect full scale) to build a voltmeter to read values of voltages up to 100 volts.
• 2.66 A 20-kΩ/V voltmeter reads 10 V full scale.
  • (a) What series resistance is required to make the meter read 50 V full scale?
  • (b) What power will the series resistor dissipate when the meter reads full scale?
• 2.67 (a) Obtain the voltage Vo in the circuit of Fig. 2.127(a).
  • (b) Determine the voltage Vʹ o measured when a voltmeter with 6-kΩ internal resistance is connected as shown in Fig. 2.127(b).

(c) The finite resistance of the meter introduces an error into the measurement. Calculate the percent error as

$$\left|\frac{V_o - V'_o}{V_o}\right| \times 100\,\%$$

(d) Find the percent error if the internal resistance were 36 kΩ.

Figure 2.127

For Prob. 2.67.

• 2.68 (a) Find the current I in the circuit of Fig. 2.128(a). (b) An ammeter with an internal resistance of 1 Ω is inserted in the network to measure Iʹas shown in Fig. 2.128(b). What is Iʹ?
  • (c) Calculate the percent error introduced by the meter as

|×100%

_____ ^I− I^{ʹ I}

2.69 A voltmeter is used to measure Vo in the circuit in Fig. 2.129. The voltmeter model consists of an ideal voltmeter in parallel with a 250-kΩ resistor. Let Vs = 95 V, Rs = 25 kΩ, and R¹ = 40 kΩ. Calculate Vo with and without the voltmeter when

(a)

$$R_2 = 5 \text{ k}\Omega$$

(b) $R_2 = 25 \text{ k}\Omega$

Figure 2.129 For Prob. 2.69.

• 2.70 (a) Consider the Wheatstone bridge shown in Fig. 2.130. Calculate va, vb, and vab.
  • (b) Rework part (a) if the ground is placed at a instead of o.

2.71 Figure 2.131 represents a model of a solar photovoltaic panel. Given that Vs = 95 V, R¹ = 25 Ω, and iL =2 A, find RL.

Figure 2.131 For Prob. 2.71.

2.72 Find Vo in the two-way power divider circuit in Fig. 2.132.

For Prob. 2.72.

2.73 An ammeter model consists of an ideal ammeter in series with a 20-Ω resistor. It is connected with a current source and an unknown resistor Rx as shown in Fig. 2.133. The ammeter reading is noted. When a potentiometer R is added and adjusted until the ammeter reading drops to one half its previous reading, then R = 65 Ω. What is the value of Rx ?

2.74 The circuit in Fig. 2.134 is to control the speed of a motor such that the motor draws currents 5 A, 3 A, and 1 A when the switch is at high, medium, and low positions, respectively. The motor can be modeled as a load resistance of 20 mΩ. Determine the series dropping resistances R1, R2, and R3.

2.75 Find Rab in the four-way power divider circuit in Fig. 2.135. Assume each R = 4 Ω.

Figure 2.133 For Prob. 2.73.

Figure 2.135 For Prob. 2.75.