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.

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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.

\[ \boxed{} \]
Transcribed Image Text: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.
Transcribed Image Text:**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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