How Does an Inductor's DC Behavior Affect Circuit Current Buildup?

[strawberrysk8]

Homework Statement

Assume that resistor R has a resistance of 34.2 Ω, inductor L has an inductance of 152 mH (milli-Henry), and the battery has a voltage of 33.7 V. Also assume that the circuit elements are ideal.

If the switch S is closed suddenly, the time for the current to attain a value of 82.1 mA is...

Homework Equations

I=I_max(1-e^(-t/T))
T=L/R

The Attempt at a Solution

I need help finding I_max.

82.1 mA=I_max(1-e^(-t/(152/34.2)))

Why do they give me V?

 

[alphysicist]

Hi strawberrysk8,

Homework Statement

Assume that resistor R has a resistance of 34.2 Ω, inductor L has an inductance of 152 mH (milli-Henry), and the battery has a voltage of 33.7 V. Also assume that the circuit elements are ideal.

If the switch S is closed suddenly, the time for the current to attain a value of 82.1 mA is...

Homework Equations

I=I_max(1-e^(-t/T))
T=L/R

The Attempt at a Solution

I need help finding I_max.

82.1 mA=I_max(1-e^(-t/(152/34.2)))

Why do they give me V?

I_max is the current in the circuit after the current has stopped changing (reached its final value). At that point, the inductor is not affecting the circuit (has no voltage drop across it). So how can you find I_max?

 

[baba89]

I would like to clarify that the given voltage (33.7 V) is not necessary for finding the maximum current in this scenario. The DC behavior of an inductor can be described by the equation I=I_max(1-e^(-t/T)), where I is the current, I_max is the maximum current, t is time, and T is the time constant, which is equal to L/R (inductance divided by resistance). Therefore, to find the maximum current, we can rearrange the equation to I_max=I/(1-e^(-t/T)). Plugging in the given values, we get I_max=82.1 mA/(1-e^(-t/(152/34.2))) = 0.0821 A/(1-e^(-4.44t)). From here, we can use algebra or a graphing calculator to solve for t. Additionally, the given voltage may be useful for calculating other aspects of the circuit, such as the power dissipated by the resistor or the energy stored in the inductor.