What Hath God Wrought?: Electric Circuits

Electric Circuits

Exercise1-2
Question.
The total charge that has entered an element is q=q(o)e^(-2t),t>=0. Find the current. Note that q(0) is the charge at t=0.

Exercise1-3
Question
Find the charge that has entered a terminal between t=0 and t=5 s when i=10t^2 A, t>=0.

Exercise1-4

Question
The total charge q(t), in coulombs, that has entered the terminal of an element is
q(t) = 0, t<0
q(t) = 2t, 0=<t=<2
q(t) = 3+e^((-2)(t-2)), t>2

SI = Système International d'Unités or the International System of Units.

Exercise1-5

Question
Find the number of picoseconds in 10 milliseconds.
Exercise1-5
Answer
10^10 picoseconds.

Exercise1-6

Question
A constant current of 4 kA flows through an element. What is the charge that has passed through the element in the first millisecond?

Exercise1-7

Question
Find the work done by a constant force of 10 mN applied to a mass of 150 grams for a distance of 50 cm.

Exercise1-8

Question
A current of 5*10^(-6) A flows through a wire. (a) How many coulombs of charge have passed through the wire in 10 seconds? (b) How many coulombs would pass through the wire in 2 years?

1-5. Voltage.

The voltage across an element is the work (energy) required to move a unit positive charge from the - terminal to the + terminal. The unit of voltage is the volt, V.

Power measures the rate at which energy is transformed, dw/dt.

Energy is the capacity to perform work, v=dw/dq, where dw is the incremental change in energy.

Exercise1-9

Question

Find the energy required to move 2 coulombs of charge through a constant voltage of 4 volts?

Exercise1-10

Question

A current of i=10A is delivered to an element for 5 s. Find the energy required to maintain a voltage of 10 volts?

Exercise1-11

Question

A 110-V electric light bulb is connected to the terminals of a bank of storage batteries producing 110 V. The current through the bulb is 6/11 A. Find the energy delivered to the bulb during a 1-s period.?

1-6Power and energy

Power is the time rate of expending or absorbing energy.

Exercise1-12

Question

Find the power and the energy for the first 10 seconds of operation of the element shown in absorbed figure when v=10 V and i=20 A.

Exercise1-13

Question

Find the power and energy supplied during the first 10 seconds of operation for the element shown in exercise1-12 when v=50e^(-10t) V and i=5e^(-10t) A. The circuit begins operation at t=0.

Exercise1-14

Question

A hydroeletric power plant can deliver power to remote users. A representation of the power plant is shown in Figure Excercise 1-12. If v=100kV and i=120A, find the power supplied by the hydroelectric plant and the energy supplied each day.

Exercise2-1
Question
Determine whether the following element is linear. v=di/dt.

Exercise2-2

Question

Show that the following element is nonlinear.

v=Ri, i>=0

v=0, i<0

Exercise2-3a
Question
The voltage-current relationship for two elements is shown in Figure. Determine a linear model for each element and indicate the range of linearity. Assume that the elements of Fig. normally operate around i=0.

Exercise2-3b
Question
The voltage-current relationship for two elements is shown in Figure. Determine a linear model for each element and indicate the range of linearity. Assume that the elements of Fig. normally operate around i=0.

Exercise2-4
Question
An active element is shown in Figure below. Find the energy supplied during the period from 0 to 10s when v=3e^(-t) V and i=2e^(-t) A

Exercise2-5

Question

The current entering the positive terminal of an element is i=-3e^(-2t) A and the voltage across the element is v=5i V for i>=0. Find whether the energy is delivered to or supplied by the element between t=0 and t=2 s. Determine the total energy between 0 and 2 s. Is the element active or passive. Assume i=v=0 for t<0.

Exercise2-6

Question

Find the power absorbed by a 100-ohm resistor when it is connected directly across a constant 10-V source.

Exercise2-7
Question
A voltage source v=10cos(t) V is connected across a resistor of 10 ohms. Find the power delivered to the resistor.

Exercise2-8a

Question

The current entering a resistor terminal is 1m A, and the resistance is 1k Ohm.Find

a).The voltage across the resistor.

Exercise2-8b

Question

The current entering a resistor terminal is 1m A, and the resistance is 1k Ohm.Find

b).The power absorbed by the resistor.

Exercise2-8c

Question

The current entering a resistor terminal is 1m A, and the resistance is 1k Ohm.Find

c).The conductance of the resistor.

Exercise2-9

Question

Find the minimum required power rating of a resistor when R=10 k Ohm and v= 100 V

Exercise2-10

Question

Find the power absorbed by the CCCS in Figure. Hint: The controlling element of this dependent source is a short circuit. The voltage across a short circuit is zero. Hence the power absorbed by the controlling element is zero. How much power is absorbed by the controlled element?

Exercise2-11

Question

Find the power delivered to the VCVS in Figure.

Exercise2-12

Question

Find the power supplied by the VCCS in Figure.

Exercise2-13

Question

Find the power absorbed by the CCVS in Figure.

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Exercise2-14

The circuit representing the electric motor and battery is shown in Figure. Find the power absorbed by the electric motor when V=12 V.and Ic=5 A

Exercise2-15

For the potentiometer circuit of Figure, calculate the meter voltage, Vm when angle=45 degree, Rp= 20k Ohm, and I= 2m Amperes.

Exercise2-16

The voltage and current of an AD590 temperature sensor are 10 V and 280 micro Amperes, respectively. Determine the measured temperature.

Exercise2-17

What is the value of the current i in Figure. At time t= 1s? At time t=5s?

Exercise2-18
What is the value of the current i in Figure. At time t=4 seconds?

Exercise2-19

What is the value of the voltage v in Figure. At time t=4 s? At t=6 s?

Exercise2-20

What is the value of the current i in Figure. At time t=1 s? At t=3 s?

Exercise3-1

For the circuit in Figure. Find i2 and v2 when v3=6 V.

Exercise3-2

Find the voltages V1 and V2 in the circuit shown in Figure.

Exercise3-3

For the circuit of Figure, Find the voltage V3 and the current i and show that the power delivered to the three resistors is equal to that supplied by the source.

Exercise3-4

Consider the voltage divider shown in Figure when R1=6 ohms. It is desired that the output power absorbed by R1=6 ohms be 6 watts. Find the voltage Vo and the required source Vs.

Exercise3-5

Again consider the voltage divider shown in Figure. Determine the required R1 when it is desired that Vo/Vs =1/6.

Exercise3-6

Consider the voltage divider shown in Figure. Determine the required Ro so that one-half of the power supplied by the source is absorbed by Ro.

Exercise3-7

Determine the equivalent resistance for the series connection of resistors shown in Figure.

Exercise3-8

A resistor network consisting of parallel resistors is shown in a package used for printed circuit board electronics in Figure. This package is only 2 cm*0.7 cm and each resistor is 1 k ohm. The circuit is connected to use four resistors as shown in Figure. Find the equivalent circuit for this network. Determine the current in each resistor when current source = 1 m Ampere.