## Useful Constants- Coulomb's constant (\( k \)): \[ k = 9.00 \times 10^9 \, \frac{N \cdot m^2}{C^2} \]- Permittivity of free space (\( \varepsilon_0 \)): \[ \varepsilon_0 = 8.85 \times 10^{-12} \, \frac{C^2}{N \cdot m^2} \]- Elementary charge (\( e \)): \[ e = 1.6 \times 10^{-19} \, C \]- Electron mass (\( m_e \)): \[ m_e = 9.11 \times 10^{-31} \, kg \]- Proton mass (\( m_p \)): \[ m_p = 1.67 \times 10^{-27} \, kg \]- Neutron mass (\( m_n \)): \[ m_n = 1.68 \times 10^{-27} \, kg \]These constants are fundamental in physics, particularly in the fields of electromagnetism and particle physics. **Circuit Analysis Problem**For the circuit shown in the diagram, the switch \( S \) is initially open and the voltage across the capacitor is \( 60 \, \text{V} \). The switch is then closed at time \( t = 0 \, \text{s} \). What is the charge on the capacitor when the current in the circuit is \( 20 \, \mu \text{A} \)?**Circuit Description:**- Capacitor: \( 22 \, \mu \text{F} \)- Resistor: \( 1.5 \, \text{M}\Omega \)**Multiple Choice Answers:**- \( 140 \, \mu \text{C} \)- \( 290 \, \mu \text{C} \)- \( 310 \, \mu \text{C} \)- \( 970 \, \mu \text{C} \)- \( 660 \, \mu \text{C} \)**Solution Explanation:**To solve for the charge on the capacitor when the current is \( 20 \, \mu \text{A} \), we use the formula for the charging process of an RC circuit:1. Implement the time constant \(\tau = R \times C\)2. Use the relationship for charge \( Q \) at a given time with current \( I \): \[ Q = C \times V \] And since the current \( I = \frac{dQ}{dt} \), integrate as needed.**Note:** This theoretical approach involves understanding the exponential nature of capacitor charging and the application of Ohm's Law (\( V = I \times R \)) in transient analysis.

Given: Voltage across capacitor, V=60 V Capacitance, C=22 μF = 22×10-6 F Resistance, R=1.5 MΩ =…

For the circuit shown in the figure below, the switch S is initially open and the voltage across the capacitor is 60 V. The switch is then closed at time t = 0 s. What is the charge on the capacitor when the current in the circuit is 20 µA? 22 µF 1.5 MQ Ο 140 μC Ο 290 μC Ο 310 μ Ο 970 μC Ο 660 μ ww

For the circuit shown in the figure below, the switch S is initially open and the voltage across the capacitor is 60 V. The switch is then closed at time t = 0 s. What is the charge on the capacitor when the current in the circuit is 20 µA? 22 µF 1.5 MQ Ο 140 μC Ο 290 μC Ο 310 μ Ο 970 μC Ο 660 μ ww

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: Switch S in in the figure is closed at time t = 0, to begin charging an initially uncharged…

Q: V 1 , V 2 , V 3 , and I1 , I2 , I3 apply to the respective resisters. V C and Q refer to the…

A: It is given that

Q: A capacitor of capacitance C = 1 μF has been charged so that the potential difference between its…

Q: Consider the circuit shown in the diagram. Before the switch is closed, both capacitors are…

A: Immediately after the switch is closed the capacitor will act as short i.e. capacitor will have zero…

Q: В 30 Ω

Q: Given the following circuit: R www C2 C1 3 Where C₁ = 6mF C₂ = 12 mF R = 145 2 € = 18 V At the…

A: Step 1:Capacitors C1 and C2 are in parallel, So the equivalent capacitance Ceq…

Q: Q 2. The circuit in the diagram R1 contains R1 = 2 kN, R2 = 3kN, C1 = 2 µF, C2 = 3 µF and ɛ = on…

A: Given: The circuit diagram is as follows. R1=2 kΩ, R2=3 kΩ, C1=2 μF, C2=3 μF, ε=120 V Introduction:…

Q: The switch S in the circuit shown below has been open for a long time when, at time t = 0, it is…

A: Given: R1 = 110 ohm R2 = 220 ohm R3 = 330 ohm C1 = 40 microfarad C2 = 80 microfarad

Q: Four capacitors having capacitances of 2 µF, 6 µF, 14 µF and 5 µF are connected in parallel and this…

Q: Don't use chat gpt It Chatgpt means downvote

A: To provide what is best and to understand more about the students concerns for their studies.

Q: A circuit contains a 6.0-battery, a 4.0-0 resistor, a 0.60-pF capacitor, and a switch in series.…

Q: Using the actual resistance values shown below, determine the Equivalent Resistance for the complex…

A: Given that:- The series and parallel combination of resistances are given in the question. We have…

Q: Consider the circuit shown in the figure below, where C, = 8.00 pF, C, = 6.00 µF, and AV = 22.0 V.…

Q: A charged capacitor is connected to a resistor and a switch as in the figure below. The circuit has…

Q: Two resistors, R1 = 2.00 kΩ and R2 = 3.00 kΩ, are connected in parallel and their combination is…

Q: In the circuit shown below, after the switch has been closed for a long time the energy stored in…

Q: The capacitor in the circuit is initially uncharged. The switch closes at time t = 0. R 4.7 kQ The…

A: Given. R = 4700 ohm Q = CV V = IR

Q: A 2.0-μF capacitor that is initially uncharged is charged through a 50-kΩ resistor. How long does it…

A: Value of capacitor C = 2μF Value of resistance R = 50kΩ Now Q =90%Q0

Q: A capacitor of capacitance C = 3 uF has been charged so that the potential difference between its…

A: Given that:- Capacitance of the capacitor=3uF

Q: R1 R1 Repeating to infinity R2 R2- R1 R1 9Ω and R, 182 extends to infinity %3D %3D A network of…

A: Given : Network of resistors of resistance R1 = 9 ohm R2 = 10 ohm We have to calculate the…

Q: 3.0 µF, and R = 2.0 . At sometime after the switch is closed, the voltage across the V. What is the…

A: Voltage by battery, Capacitance, Resistance,…

Q: The diagram represents an electric circuit consisting of a 12-volt battery, a 3.0-ohm resistor, R1,…

Question

## Useful Constants

- Coulomb's constant (\( k \)):
\[
k = 9.00 \times 10^9 \, \frac{N \cdot m^2}{C^2}
\]

- Permittivity of free space (\( \varepsilon_0 \)):
\[
\varepsilon_0 = 8.85 \times 10^{-12} \, \frac{C^2}{N \cdot m^2}
\]

- Elementary charge (\( e \)):
\[
e = 1.6 \times 10^{-19} \, C
\]

- Electron mass (\( m_e \)):
\[
m_e = 9.11 \times 10^{-31} \, kg
\]

- Proton mass (\( m_p \)):
\[
m_p = 1.67 \times 10^{-27} \, kg
\]

- Neutron mass (\( m_n \)):
\[
m_n = 1.68 \times 10^{-27} \, kg
\]

These constants are fundamental in physics, particularly in the fields of electromagnetism and particle physics.

**Circuit Analysis Problem**

For the circuit shown in the diagram, the switch \( S \) is initially open and the voltage across the capacitor is \( 60 \, \text{V} \). The switch is then closed at time \( t = 0 \, \text{s} \). What is the charge on the capacitor when the current in the circuit is \( 20 \, \mu \text{A} \)?

**Circuit Description:**

- Capacitor: \( 22 \, \mu \text{F} \)
- Resistor: \( 1.5 \, \text{M}\Omega \)

**Multiple Choice Answers:**

- \( 140 \, \mu \text{C} \)
- \( 290 \, \mu \text{C} \)
- \( 310 \, \mu \text{C} \)
- \( 970 \, \mu \text{C} \)
- \( 660 \, \mu \text{C} \)

**Solution Explanation:**

To solve for the charge on the capacitor when the current is \( 20 \, \mu \text{A} \), we use the formula for the charging process of an RC circuit:

1. Implement the time constant \(\tau = R \times C\)

2. Use the relationship for charge \( Q \) at a given time with current \( I \):

\[
Q = C \times V
\]

And since the current \( I = \frac{dQ}{dt} \), integrate as needed.

**Note:** This theoretical approach involves understanding the exponential nature of capacitor charging and the application of Ohm's Law (\( V = I \times R \)) in transient analysis.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

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

Similar questions

For the network shown, completely fill the table below, if a 120-V source were connected across the open end of the circuit. R1 NA R2 R4 AMA R3 R. 요 1, A V, V P, W Ri 1.0 R2 2.0 R3 3.0 R4 4.0 RT 120
Problem 4: A current of I = 2.3 A passes through the circuit shown, where R = 95 Q. I 3R 5R ww ww 2R 6R 2R 7R ww ww 10R 5R Part (a) In terms of R, I, and numeric values, write an expression for the voltage of the source, V. Expression : V = Select from the variables below to write your expression. Note that all variables may not be required. a, B, 0, a, d, g, h, I, j, k, m, P, R, S, t Part (b) What is the voltage, Vin volts? Numeric : A numeric value is expected and not an expression. V =
82. Switch S in is closed at time t 30, to begin charging an initially uncharged capacitance C= 15.0 µF through a resistor of resistance R = 20.0 Q. %3D S. cаpacitor of R %3D At what time is the potential across the capacitor equal to that across the resistor?
The switch given has been closed for a very long time.a. What is the charge on the capacitor?b. The switch is opened at t = 0 s. At what time has the charge on the capacitor decreased to 10% of its initial value?
R C 3. From the figure above, a switch is closed at time t = 0, allowing the capacitor to begin charging. The capacitance of the capacitor is given a value of C = 10 µF with a resistor of resistance R= 10N. At what time is the potential across the capacitor equal to the potential across the resistor?
A circuit diagram is shown in the figure below. You do not need to solve the whole circuit for the following questions. 1122 13 Q2 M 6.0 V E + g 0.20A 15 92 m 1992 W 1992 0.40 A b 11 0.10A ← What is the emf of the battery between points d and g? [Select] m 30 22 w 25 92 m 21 22 21.0 V 14.0 V + C 1892 10.70A h Use the current direction assumed in the diagram. What is the current I₂? [Select] Point g is grounded (i.e., V₂ = 0 V), as shown in the diagram. What is the electric potential at point f? [Select]
In the circuit shown in the figure attached each capacitor initially has a charge of magnitude 4.00 nC on its plates. a) After the switch S is closed, what will be the current in the circuit at the instant that the capacitors have lost 80.0% of their initial stored energy?
A current of I= 3.5 A passes through the circuit shown, where R = 35 2. 3R 5R wW (v 2R 6R : 2R 7R ww 5R 10R In terms of R, I, and numeric values, write an expression for the voltage of the source, V. V = What is the voltage, V in volts? V =
For the circuit shown below; fill in the table of values for V, I, R and P. You must show all your work
Each resistor in the three circuits in the drawing has the same resistance R, and the batteries have the same voltage V. The values for R and Vare 50 and 6.0 V, respectively. Determine the total power delivered by the battery in each of the three circuits. PA= i PB = i Pc i R www R www R wwww R P Circuit A R www R R F V Circuit C R ww wwwww R www R R www R www R Circuit B R
!! The circuit in the figure below has been connected for a long time. Let R, = 12 Q, R, = 9 N, and V = 16volts. 1.00 N R1 1.00 µF R2 2.00 N RC1 (a) Find the Charye on the capacitor. Q = HC (b) If the battery is disconnected from the circuit, what is the time constant when the capacitor discharges? T3D sr (c) Over what time interval does the capacitor discharge to 0.35 of its initial charge? Time =
For the circuit shown in the figure, V = 20 V, C = 10 μF, R = 0.80 MQ, and the battery is ideal. Initially the switch S is open and the capacitor is uncharged. The switch is then closed at time t = 0.00 s. What is the charge across the capacitor 20 s after closing the switch? { www R O 0.18 mC O 1.5 mC O 0.48 mC O 3.0 MC O 2.3 MC