Problems

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Problems

Section 1.3 Charge and Current

• 1.1 How much charge is represented by these number of electrons?
  • (a) 6.482 × 10¹⁷
  • (b) 1.24 × 1018
  • (c) 2.46 × 1019
  • (d) 1.628 × 1020
• 1.2 Determine the current flowing through an element if the charge flow is given by
  • (a) q(t) = (3) mC

(b)

$$q(t) = (4t^2 + 20t - 4)$$

C

(c)

$$q(t) = (15e^{-3t} - 2e^{-18t}) nC$$

(d) $q(t) = 5t^2(3t^3 + 4) pC$

(d)

$$q(t) = 5t^2(3t^3 + 4) \text{ pC}$$

(e) $q(t) = 2e^{-3t} \sin(20\pi t) \mu\text{C}$

1.3 Find the charge q(t) flowing through a device if the current is:

(a)

$$i(t) = 3$$

A, $q(0) = 1$ C
\n(b) $i(t) = (2t + 5)$ mA, $q(0) = 0$
\n(c) $i(t) = 20 \cos(10t + \pi/6) \mu$ A, $q(0) = 2 \mu$ C
\n(d) $i(t) = 10e^{-30t} \sin 40t$ A, $q(0) = 0$

• 1.4 A total charge of 300 C flows past a given cross section of a conductor in 30 seconds. What is the value of the current?
• 1.5 Determine the total charge transferred over the time interval of 0 ≤ t ≤ 10 s when i(t) = __1 2 t A.
• 1.6 The charge entering a certain element is shown in Fig. 1.23. Find the current at:

(a)

$$t = 1$$

ms (b) $t = 6$ ms (c) $t = 10$ ms

1.7 The charge flowing in a wire is plotted in Fig. 1.24. Sketch the corresponding current.

Figure 1.24

For Prob. 1.7.

1.8 The current flowing past a point in a device is shown in Fig. 1.25. Calculate the total charge through the point.

Figure 1.25

For Prob. 1.8.

1.9 The current through an element is shown in Fig. 1.26. Determine the total charge that passed through the element at:

For Prob. 1.9.

Sections 1.4 and 1.5 Voltage, Power, and Energy

• 1.10 A lightning bolt with 10 kA strikes an object for 15 μs. How much charge is deposited on the object?
• 1.11 A rechargeable flashlight battery is capable of delivering 90 mA for about 12 h. How much charge can it release at that rate? If its terminal voltage is 1.5 V, how much energy can the battery deliver?
• 1.12 If the current flowing through an element is given by

$$i(t) = \begin{cases} 3tA, & 0 \le t < 6 \text{ s} \\ 18A, & 6 \le t < 10 \text{ s} \\ -12A, & 10 \le t < 15 \text{ s} \\ 0, & t \ge 15 \text{ s} \end{cases}$$

Plot the charge stored in the element over 0 < t < 20 s.

1.13 The charge entering the positive terminal of an element is

$$q = 5\sin 4\pi t \,\mathrm{mC}$$

while the voltage across the element (plus to minus) is

$$v = 3\cos 4\pi t \,\mathrm{V}$$

• (a) Find the power delivered to the element at t = 0.3 s.
• (b) Calculate the energy delivered to the element between 0 and 0.6 s.
• 1.14 The voltage v(t) across a device and the current i(t) through it are

$$v(t) = 20 \sin(4t)$$

V and $i(t) = 10(1 + e^{-2t})$ mA

Calculate:

• (a) the total charge in the device at t = 1 s, q(0) = 0.
• (b) the power consumed by the device at t = 1 s.
• 1.15 The current entering the positive terminal of a device is i(t) = 6e⁻2*^t* mA and the voltage across the device is v(t) = 10di∕dtV.
  • (a) Find the charge delivered to the device between t = 0 and t = 2 s.
  • (b) Calculate the power absorbed.
  • (c) Determine the energy absorbed in 3 s.

Section 1.6 Circuit Elements

• 1.16 Figure 1.27 shows the current through and the voltage across an element.
  • (a) Sketch the power delivered to the element for t > 0.
  • (b) Fnd the total energy absorbed by the element for the period of 0 < t < 4s.

Figure 1.27 For Prob. 1.16.

1.17 Figure 1.28 shows a circuit with four elements, p¹ = 60 W absorbed, p³ = −145 W absorbed, and p⁴ = 75 W absorbed. How many watts does element 2 absorb?

Figure 1.28

For Prob. 1.17.

1.18 Find the power absorbed by each of the elements in Fig. 1.29.

Figure 1.29

For Prob. 1.18.

1.19 Find I and the power absorbed by each element in the network of Fig. 1.30.

Figure 1.30

For Prob. 1.19.

1.20 Find Vo and the power absorbed by each element in the circuit of Fig. 1.31.

For Prob. 1.20.

Section 1.7 Applications

• 1.21 A 60-W incandescent bulb operates at 120 V. How many electrons and coulombs flow through the bulb in one day?

• 1.22 A lightning bolt strikes an airplane with 40 kA for 1.7 ms. How many coulombs of charge are deposited on the plane?

• 1.23 A 1.8-kW electric heater takes 15 min to boil a quantity of water. If this is done once a day and power costs 10 cents/kWh, what is the cost of its operation for 30 days?

• 1.24 A utility company charges 8.2 cents/kWh. If a consumer operates a 60-W light bulb continuously for one day, how much is the consumer charged?

• 1.25 A 1.2-kW toaster takes roughly 4 minutes to heat four slices of bread. Find the cost of operating the toaster twice per day for 2 weeks (14 days). Assume energy costs 9 cents/kWh.

• 1.26 A cell phone battery is rated at 3.85 V and can store 10.78 watt-hours of energy.

  • (a) How much average current can it deliver over a period of 3 hours if it is fully discharged at the end of that time?
  • (b) How much average power is delivered in part (a)?
  • (c) What is the ampere-hour rating of the battery?

• 1.27 A constant current of 3 A for 4 hours is required to charge an automotive battery. If the terminal voltage is 10 + t∕2V, where t is in hours,

  • (a) how much charge is transported as a result of the charging?

• (b) how much energy is expended?

• (c) how much does the charging cost? Assume electricity costs 9 cents/kWh.

• 1.28 A 150-W incandescent outdoor lamp is connected to a 120-V source and is left burning continuously for an average of 12 hours per day. Determine:

  • (a) the current through the lamp when it is lit.
  • (b) the cost of operating the light for one non-leap year if electricity costs 9.5 cents per kWh.

• 1.29 An electric stove with four burners and an oven is used in preparing a meal as follows.

Burner 1: 20 minutes	Burner 2: 40 minutes
Burner 3: 15 minutes	Burner 4: 45 minutes
Oven: 30 minutes

If each b urner is rated at 1.2 kW and the o ven at 1.8 kW, and electricity costs 12 cents per kWh, calculate the cost of electricity used in preparing the meal.

1.30 Reliant Energy (the electric company in Houston, Texas) charges customers as follows:

Monthly charge $6 First 250 kWh @ $0.02/kWh All additional kWh @ $0.07/kWh

If a customer uses 2,436 kWh in one month, ho w much will Reliant Energy charge?

1.31 In a household, a business is run for an average of 6 h/day. The total power consumed by the computer and its printer is 230 W. In addition, a 75-W light runs during the same 6 h. If their utility charges 11.75 cents per kWh, how much do the owners pay every 30 days?