Respuesta :
Answer:
(a). The initial rate is 2.60 A/s.
(b). The rate of current increases is 0.8658 A/s.
(c). The current is 0.435 A.
(d). The final steady-state current is 0.75 A.
Explanation:
Given that,
Inductance = 2.30 H
Resistance = 8.00 Ω
Voltage = 6.00 V
(a). We need to calculate the initial rate of increase of current in the circuit.
Using formula of initial rate
[tex]V=initial\ rate\times inductance[/tex]
[tex]initial\ rate=\dfrac{V}{L}[/tex]
Put the value into the formula
[tex]initial \rate=\dfrac{6.00}{2.30}[/tex]
[tex]initial\ rate=2.60\ A/s[/tex]
The initial rate is 2.60 A/s.
(b). We need to calculate the rate of increase of current at the instant when the current is 0.500
Using formula of rate of increase of current
[tex]rate\ of \ current\ increase=initial\ rate\times e^{\dfrac{-t}{T}}[/tex]....(I)
Where, [tex]T=\dfrac{L}{R}[/tex]
[tex]T=\dfrac{2.30}{8.00}[/tex]
[tex]T=0.2875[/tex]
Using formula of current
[tex]i=\dfrac{V}{R}(1-e^{\dfrac{-t}{T}})[/tex]
[tex]e^{\dfrac{-t}{T}}=1-(i\times\dfrac{R}{V})[/tex]
[tex]e^{\dfrac{-t}{T}}=1-(0.500\times\dfrac{8.00}{6.00})[/tex]
[tex]e^{\dfrac{-t}{T}}=0.333[/tex]
The rate of current increases is
Put the value in the equation (I)
[tex]rate\ of\ current\ increase=2.60\times0.333[/tex]
[tex]rate\ of\ current\ increase=0.8658\ A/s[/tex]
The rate of current increases is 0.8658 A/s.
(c). We need to calculate the current
Using formula of current
[tex]i=\dfrac{V}{R}(1-e^{\dfrac{-t}{T}})[/tex]
Put the value into the formula
[tex]i=\dfrac{6.00}{8.00}\times(1-e^{\dfrac{-0.250}{0.2875}})[/tex]
[tex]i=0.435\ A[/tex]
The current is 0.435 A.
(d). We need to calculate the final steady-state current
Using formula of steady state
[tex]i=\dfrac{V}{R}[/tex]
[tex]i=\dfrac{6.00}{8.00}[/tex]
[tex]i=0.75\ A[/tex]
The final steady-state current is 0.75 A.
Hence, This is the required solution.
