calculate numerical value of current in inductor resistant circuit.
l=1mH r=3k (ist=1ma at t=0)
i1(t=1us)in ma. i0=1ma
my work. i=i0(1-e^-(t/T))
1*10^-3(1-e^(-1/0.33)
i=0.952ma this is wrong
do I need to add initial current to this(1ma). why is this wrong??
To calculate the numerical value of the current in an inductor resistor circuit, you can use the formula i = i0 * (1 - e^(-t/T)), where i is the current at time t, i0 is the initial current, and T is the time constant of the circuit.
In your calculation, you correctly used the formula but arrived at the wrong result. Let's examine the steps to see what went wrong:
i = i0 * (1 - e^(-t/T))
i = 1 * 10^-3 * (1 - e^(-1/0.33))
Initially, it seems that you correctly substituted the values of i0 and t. However, the issue lies in the value you used for T. The time constant of an inductor-resistor circuit is calculated as the ratio of the inductance (L) to the resistance (R), i.e., T = L/R.
Given that the inductance (L) is 1 mH (which should be converted to henries by dividing by 1000) and the resistance (R) is 3 kΩ, the correct time constant T would be:
T = L/R
T = (1 * 10^-3) / (3 * 10^3)
T = 1/3000 s
T = 0.33 μs
Now, substituting the correct value of T into the formula:
i = 1 * 10^-3 * (1 - e^(-1/0.33))
By evaluating this expression, you will find the correct numerical value for the current at t = 1 μs.
Please note that you do not need to add the initial current (i0) to the result since it is already accounted for in the formula. The formula directly gives the current at any given time t, considering the initial condition is i0 at t = 0.
Hope this clarifies the mistake in your calculation and provides a clear understanding of how to calculate the current in an inductor resistor circuit.