Explanation The initial conditions on voltage across a capacitor with capacitance C is V C ( 0.0 ) = 0 and the charge is i = 0.042 t mA with time t = 2.0 μ s . Rewrite the charge i = 0.042 t mA and the point t = 2.0 μ s as follows. i = 0.042 t mA = 0.042 t × 10 − 3 A ( ∵ 1 mA = 10 − 3 ) t = 2.0 μ s = 2 × 10 − 6 s ( ∵ 1 μ s = 10 − 6 ) Note that, the voltage across a capacitor with capacitance C is given by V C = 1 C ∫ i d t , where V C is measured in volts, C in farads, i in amperes, and t in seconds. Substitute i = 0.042 t × 10 − 3 A and C = 8.50 × 10 − 9 F in V C = 1 C ∫ i d t and simplify for V C . V C = 1 8.50 × 10 − 9 ∫ ( 0.042 t × 10 − 3 ) d t = 1 8.50 × 10 − 9 ( 0.021 × 10 − 3 ) t 2 + C 1 Apply the initial condition on voltage across a capacitor with capacitance C to obtain C 1 as follows

Basic Technical Mathematics with Calculus (11th Edition)

11th Edition

ISBN: 9780134437736

Author: Allyn J. Washington, Richard Evans

Publisher: PEARSON

See similar textbooks

Concept explainers

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

Videos

Question

Chapter 26.1, Problem 26E

To determine

The voltage after being charged by 0.042t mA for the time 2.0 μs.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 26.1, Problem 25E

Chapter 26.1, Problem 27E

Students have asked these similar questions

Explain how to solve all solutions of y"(x)+ay'(x)+by(x)=0 when the Characteristic Equation λ2+aλ+b=0 of the second-order linear differential equation y"(x)+ay'(x)+by(x)=0 has no real roots. Please distinguish between the two methods of "using real numbers to solve the space base" and "using complex numbers to solve the space base" and explain the key points respectively.

Use the circle to find exact value of each trigonometric function (number 16)

Use the circle to find exact value of each trigonometric function (number 22)

Chapter 26 Solutions

Basic Technical Mathematics with Calculus (11th Edition)

Ch. 26.1 - In Example 4, change the acceleration to a = 4...Ch. 26.1 - Prob. 2PE Ch. 26.1 - In Example 3, change 5.0 s to 2.5 s and then solve...Ch. 26.1 - Prob. 2E Ch. 26.1 - What is the velocity (in ft/s) of a sandbag 1.5 s...Ch. 26.1 - Prob. 4E Ch. 26.1 - A conveyor belt 8.00 m long moves at 0.25 m/s. If...Ch. 26.1 - Prob. 6E Ch. 26.1 - The velocity (in km/h) of a plane flying into an...Ch. 26.1 - A cyclist goes downhill for 15 min with a velocity...

Ch. 26.1 - A car crosses an intersection as a fire engine...Ch. 26.1 - In designing a highway, a civil engineer must...Ch. 26.1 - Prob. 11E Ch. 26.1 - Prob. 12E Ch. 26.1 - A certain Chevrolet Corvette goes from 0 mi/h to...Ch. 26.1 - Prob. 14E Ch. 26.1 - Prob. 15E Ch. 26.1 - Prob. 16E Ch. 26.1 - Prob. 17E Ch. 26.1 - Prob. 18E Ch. 26.1 - Prob. 19E Ch. 26.1 - Prob. 20E Ch. 26.1 - Prob. 21E Ch. 26.1 - Prob. 22E Ch. 26.1 - Prob. 23E Ch. 26.1 - Prob. 24E Ch. 26.1 - Prob. 25E Ch. 26.1 - Prob. 26E Ch. 26.1 - The voltage across a 3.75-μF capacitor in a...Ch. 26.1 - Prob. 28E Ch. 26.1 - Prob. 29E Ch. 26.1 - Prob. 30E Ch. 26.1 - Prob. 31E Ch. 26.1 - Prob. 32E Ch. 26.1 - Prob. 33E Ch. 26.1 - Prob. 34E Ch. 26.1 - Prob. 35E Ch. 26.1 - Prob. 36E Ch. 26.2 - Find the area in the first quadrant bounded by y =...Ch. 26.2 - Prob. 2PE Ch. 26.2 - In Exercises 1 and 2, make the given changes in...Ch. 26.2 - In Exercises 1 and 2, make the given changes in...Ch. 26.2 - Prob. 3E Ch. 26.2 - Prob. 4E Ch. 26.2 - Prob. 5E Ch. 26.2 - Prob. 6E Ch. 26.2 - In Exercises 3–28, find the areas bounded by the...Ch. 26.2 - Prob. 8E Ch. 26.2 - Prob. 9E Ch. 26.2 - Prob. 10E Ch. 26.2 - Prob. 11E Ch. 26.2 - Prob. 12E Ch. 26.2 - Prob. 13E Ch. 26.2 - Prob. 14E Ch. 26.2 - Prob. 15E Ch. 26.2 - Prob. 16E Ch. 26.2 - Prob. 17E Ch. 26.2 - Prob. 18E Ch. 26.2 - Prob. 19E Ch. 26.2 - Prob. 20E Ch. 26.2 - Prob. 21E Ch. 26.2 - Prob. 22E Ch. 26.2 - Prob. 23E Ch. 26.2 - Prob. 24E Ch. 26.2 - Prob. 25E Ch. 26.2 - Prob. 26E Ch. 26.2 - Prob. 27E Ch. 26.2 - Prob. 28E Ch. 26.2 - Prob. 29E Ch. 26.2 - Prob. 30E Ch. 26.2 - Prob. 31E Ch. 26.2 - In Exercises 29–38, solve the given problems. 32....Ch. 26.2 - Prob. 33E Ch. 26.2 - Prob. 34E Ch. 26.2 - Prob. 35E Ch. 26.2 - Prob. 36E Ch. 26.2 - Prob. 37E Ch. 26.2 - Prob. 38E Ch. 26.2 - Prob. 39E Ch. 26.2 - Prob. 40E Ch. 26.2 - Prob. 41E Ch. 26.2 - Prob. 42E Ch. 26.2 - Prob. 43E Ch. 26.2 - Prob. 44E Ch. 26.2 - Prob. 45E Ch. 26.2 - Prob. 46E Ch. 26.2 - Prob. 47E Ch. 26.2 - Prob. 48E Ch. 26.2 - Prob. 49E Ch. 26.2 - Prob. 50E Ch. 26.3 - Find the volume of the solid generated by...Ch. 26.3 - Prob. 2PE Ch. 26.3 - Prob. 1E Ch. 26.3 - Prob. 2E Ch. 26.3 - Prob. 3E Ch. 26.3 - Prob. 4E Ch. 26.3 - Prob. 5E Ch. 26.3 - Prob. 6E Ch. 26.3 - Prob. 7E Ch. 26.3 - Prob. 8E Ch. 26.3 - In Exercises 7–16, find the volume generated by...Ch. 26.3 - Prob. 10E Ch. 26.3 - In Exercises 7–16, find the volume generated by...Ch. 26.3 - Prob. 12E Ch. 26.3 - Prob. 13E Ch. 26.3 - Prob. 14E Ch. 26.3 - Prob. 15E Ch. 26.3 - Prob. 16E Ch. 26.3 - Prob. 17E Ch. 26.3 - Prob. 18E Ch. 26.3 - Prob. 19E Ch. 26.3 - Prob. 20E Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 17–26, find the volume generated by...Ch. 26.3 - In Exercises 27–40, find the indicated volumes by...Ch. 26.3 - Prob. 28E Ch. 26.3 - Prob. 29E Ch. 26.3 - Prob. 30E Ch. 26.3 - Prob. 31E Ch. 26.3 - Prob. 32E Ch. 26.3 - Prob. 33E Ch. 26.3 - Prob. 34E Ch. 26.3 - Prob. 35E Ch. 26.3 - Prob. 36E Ch. 26.3 - Prob. 37E Ch. 26.3 - Prob. 38E Ch. 26.3 - Prob. 39E Ch. 26.3 - Prob. 40E Ch. 26.4 - In Example 4, change y = 4 to y = 1 and solve the...Ch. 26.4 - Prob. 1E Ch. 26.4 - Prob. 2E Ch. 26.4 - In Exercises 3–6, find the center of mass (in cm)...Ch. 26.4 - Prob. 4E Ch. 26.4 - Prob. 5E Ch. 26.4 - Prob. 6E Ch. 26.4 - Prob. 7E Ch. 26.4 - Prob. 8E Ch. 26.4 - Prob. 9E Ch. 26.4 - Prob. 10E Ch. 26.4 - Prob. 11E Ch. 26.4 - Prob. 12E Ch. 26.4 - Prob. 13E Ch. 26.4 - Prob. 14E Ch. 26.4 - Prob. 15E Ch. 26.4 - Prob. 16E Ch. 26.4 - Prob. 17E Ch. 26.4 - In Exercises 11–34, find the coordinates of the...Ch. 26.4 - Prob. 19E Ch. 26.4 - In Exercises 11–34, find the coordinates of the...Ch. 26.4 - Prob. 21E Ch. 26.4 - In Exercises 11–34, find the coordinates of the...Ch. 26.4 - In Exercises 11–34, find the coordinates of the...Ch. 26.4 - In Exercises 11–34, find the coordinates of the...Ch. 26.4 - Prob. 25E Ch. 26.4 - Prob. 26E Ch. 26.4 - Prob. 27E Ch. 26.4 - Prob. 28E Ch. 26.4 - Prob. 29E Ch. 26.4 - In Exercises 11–34, find the coordinates of the...Ch. 26.4 - Prob. 31E Ch. 26.4 - Prob. 32E Ch. 26.4 - Prob. 33E Ch. 26.4 - Prob. 34E Ch. 26.5 - EXAMPLE 1 Moment of inertia and radius of...Ch. 26.5 - Prob. 1E Ch. 26.5 - Prob. 2E Ch. 26.5 - Prob. 3E Ch. 26.5 - Prob. 4E Ch. 26.5 - Prob. 5E Ch. 26.5 - Prob. 6E Ch. 26.5 - Prob. 7E Ch. 26.5 - Prob. 8E Ch. 26.5 - Prob. 9E Ch. 26.5 - Prob. 10E Ch. 26.5 - In Exercises 7–28, find the indicated moment of...Ch. 26.5 - In Exercises 7–28, find the indicated moment of...Ch. 26.5 - Prob. 13E Ch. 26.5 - Prob. 14E Ch. 26.5 - Prob. 15E Ch. 26.5 - In Exercises 7–28, find the indicated moment of...Ch. 26.5 - Prob. 17E Ch. 26.5 - Prob. 18E Ch. 26.5 - Prob. 19E Ch. 26.5 - Prob. 20E Ch. 26.5 - In Exercises 7–28, find the indicated moment of...Ch. 26.5 - Prob. 22E Ch. 26.5 - Prob. 23E Ch. 26.5 - Prob. 24E Ch. 26.5 - Prob. 25E Ch. 26.5 - Prob. 26E Ch. 26.5 - Prob. 27E Ch. 26.5 - Prob. 28E Ch. 26.6 - Prob. 1PE Ch. 26.6 - Prob. 2PE Ch. 26.6 - Prob. 1E Ch. 26.6 - Prob. 2E Ch. 26.6 - Prob. 3E Ch. 26.6 - Prob. 4E Ch. 26.6 - Prob. 5E Ch. 26.6 - Prob. 6E Ch. 26.6 - An electron has a 1.6 × 10–19 C negative charge....Ch. 26.6 - Prob. 8E Ch. 26.6 - Prob. 9E Ch. 26.6 - Prob. 10E Ch. 26.6 - Prob. 11E Ch. 26.6 - Prob. 12E Ch. 26.6 - At liftoff, a rocket weighs 32.5 tons, including...Ch. 26.6 - Prob. 14E Ch. 26.6 - Prob. 15E Ch. 26.6 - Prob. 16E Ch. 26.6 - Prob. 17E Ch. 26.6 - Prob. 18E Ch. 26.6 - Prob. 19E Ch. 26.6 - Prob. 20E Ch. 26.6 - Prob. 21E Ch. 26.6 - Prob. 22E Ch. 26.6 - Prob. 23E Ch. 26.6 - Prob. 24E Ch. 26.6 - Prob. 25E Ch. 26.6 - Prob. 26E Ch. 26.6 - Prob. 27E Ch. 26.6 - Prob. 28E Ch. 26.6 - Prob. 29E Ch. 26.6 - Prob. 30E Ch. 26.6 - Prob. 31E Ch. 26.6 - Prob. 32E Ch. 26.6 - Prob. 33E Ch. 26.6 - Prob. 34E Ch. 26.6 - Prob. 35E Ch. 26.6 - Prob. 36E Ch. 26.6 - Prob. 37E Ch. 26.6 - Prob. 38E Ch. 26 - Prob. 1RE Ch. 26 - Prob. 2RE Ch. 26 - Prob. 3RE Ch. 26 - Prob. 4RE Ch. 26 - Prob. 5RE Ch. 26 - Prob. 6RE Ch. 26 - Prob. 7RE Ch. 26 - Prob. 8RE Ch. 26 - Prob. 9RE Ch. 26 - Prob. 10RE Ch. 26 - Prob. 11RE Ch. 26 - Prob. 12RE Ch. 26 - Prob. 13RE Ch. 26 - Prob. 14RE Ch. 26 - Prob. 15RE Ch. 26 - Prob. 16RE Ch. 26 - Prob. 17RE Ch. 26 - Prob. 18RE Ch. 26 - Prob. 19RE Ch. 26 - Prob. 20RE Ch. 26 - Prob. 21RE Ch. 26 - Prob. 22RE Ch. 26 - Prob. 23RE Ch. 26 - Prob. 24RE Ch. 26 - Prob. 25RE Ch. 26 - Prob. 26RE Ch. 26 - Prob. 27RE Ch. 26 - Prob. 28RE Ch. 26 - Prob. 29RE Ch. 26 - Prob. 30RE Ch. 26 - Prob. 31RE Ch. 26 - Prob. 32RE Ch. 26 - Prob. 33RE Ch. 26 - Prob. 34RE Ch. 26 - Prob. 35RE Ch. 26 - Prob. 36RE Ch. 26 - Prob. 37RE Ch. 26 - Prob. 38RE Ch. 26 - Prob. 39RE Ch. 26 - Prob. 40RE Ch. 26 - Prob. 41RE Ch. 26 - Prob. 42RE Ch. 26 - Prob. 43RE Ch. 26 - Prob. 44RE Ch. 26 - Prob. 45RE Ch. 26 - Prob. 46RE Ch. 26 - Prob. 47RE Ch. 26 - Prob. 48RE Ch. 26 - Prob. 49RE Ch. 26 - Prob. 50RE Ch. 26 - Prob. 51RE Ch. 26 - Prob. 52RE Ch. 26 - Prob. 53RE Ch. 26 - Prob. 54RE Ch. 26 - Prob. 55RE Ch. 26 - Prob. 56RE Ch. 26 - Prob. 57RE Ch. 26 - Prob. 58RE Ch. 26 - Prob. 59RE Ch. 26 - Prob. 60RE Ch. 26 - Prob. 61RE Ch. 26 - Prob. 62RE Ch. 26 - Prob. 63RE Ch. 26 - Prob. 64RE Ch. 26 - Prob. 65RE Ch. 26 - Prob. 1PT Ch. 26 - Prob. 2PT Ch. 26 - Prob. 3PT Ch. 26 - Prob. 4PT Ch. 26 - Prob. 5PT Ch. 26 - Prob. 6PT Ch. 26 - Prob. 7PT Ch. 26 - Prob. 8PT Ch. 26 - Prob. 9PT Ch. 26 - Prob. 10PT

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The voltage after being charged by 0.042 t mA for the time 2.0 μ s .

Concept explainers

Videos

The voltage after being charged by 0.042t mA for the time 2.0 μs.

Want to see the full answer?

Chapter 26 Solutions