The total amount of charge in Coulombs that has entered a wire at time \( t \) is given by the expression \( Q = 11.1(1 - e^{-t/3}) \), where \( t \) is in seconds. What is the current (in units of Amperes) in the wire at \( t = 1 \, \text{s} \)? Please enter only the numerical value, and keep it to one decimal place, i.e., X.X, and do not include the units.\[ \boxed{} \] **Useful Constants:**- \( k = 9.00 \times 10^9 \, \frac{\text{Nm}^2}{\text{C}^2} \) *Coulomb's constant, used in calculating the electric force between two charges.*- \( \varepsilon_0 = 8.85 \times 10^{-12} \, \frac{\text{C}^2}{\text{Nm}^2} \) *Permittivity of free space, fundamental in electromagnetic theory.*- \( e = 1.6 \times 10^{-19} \, \text{C} \) *Elementary charge, the magnitude of charge of an electron.*- \( m_e = 9.11 \times 10^{-31} \, \text{kg} \) *Mass of an electron.*- \( m_p = 1.67 \times 10^{-27} \, \text{kg} \) *Mass of a proton.*- \( m_n = 1.68 \times 10^{-27} \, \text{kg} \) *Mass of a neutron.*These constants are foundational in physics, particularly in calculations involving electromagnetism and particle physics.

Write the expression of the charge. Q=11.11-e-t/3

The total amount of charge in Coulombs that has entered a wire at time t is given by the expression Q =11.1(1 – e¯³), where t is in seconds. What is the current (in units of Amperes) in the wire at t = 1 s? Please enter only the numerical value, and keep it to one decimal place, i.e., X.X, and do not include the units.

The total amount of charge in Coulombs that has entered a wire at time t is given by the expression Q =11.1(1 – e¯³), where t is in seconds. What is the current (in units of Amperes) in the wire at t = 1 s? Please enter only the numerical value, and keep it to one decimal place, i.e., X.X, and do not include the units.

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)...

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Concept explainers

Microscopic view of current

In physics, the term current is expressed as the rate of flow of electric charges across the area per unit time (I=q/t). It propagates along in the direction of the motion of positive charges. When the current is caused by the motion of electrons, the direction of the current is opposite to the flow.

Question

The total amount of charge in Coulombs that has entered a wire at time \( t \) is given by the expression \( Q = 11.1(1 - e^{-t/3}) \), where \( t \) is in seconds. What is the current (in units of Amperes) in the wire at \( t = 1 \, \text{s} \)? Please enter only the numerical value, and keep it to one decimal place, i.e., X.X, and do not include the units.

\[ \boxed{} \]

**Useful Constants:**

- \( k = 9.00 \times 10^9 \, \frac{\text{Nm}^2}{\text{C}^2} \)
*Coulomb's constant, used in calculating the electric force between two charges.*

- \( \varepsilon_0 = 8.85 \times 10^{-12} \, \frac{\text{C}^2}{\text{Nm}^2} \)
*Permittivity of free space, fundamental in electromagnetic theory.*

- \( e = 1.6 \times 10^{-19} \, \text{C} \)
*Elementary charge, the magnitude of charge of an electron.*

- \( m_e = 9.11 \times 10^{-31} \, \text{kg} \)
*Mass of an electron.*

- \( m_p = 1.67 \times 10^{-27} \, \text{kg} \)
*Mass of a proton.*

- \( m_n = 1.68 \times 10^{-27} \, \text{kg} \)
*Mass of a neutron.*

These constants are foundational in physics, particularly in calculations involving electromagnetism and particle physics.

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