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## Explanation & Answer

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Math265 Project Part B

Name:

In this part of the project, you will model the behavior of a resistor-inductor (RL) circuit in a transient

state.

Initially, the DC voltage source is off and there is no current in the circuit. After the source ‘ε’ is turned

on, the current through the inductor quickly rises and produces an EMF that opposes the change in

current:

𝑉𝐿 = 𝐿

𝑑𝑖

𝑑𝑡

where ‘L’ is the inductance

Using Kirchhoff’s Voltage Law and Ohm’s Law results in the equation

𝜀 − 𝐼𝑅 − 𝐿

𝑑𝑖

=0

𝑑𝑡

This differential equation can be solved to determine an expression for the current through the circuit as

a function of time:

𝑡

𝐼(𝑡) = 𝐼𝐹 [1 − 𝑒 − ⁄𝜏𝐿 ]

𝜀

where 𝐼𝐹 = 𝑅 is the final current and 𝜏𝐿 = 𝐿⁄𝑅 is known as the inductive time constant.

The theoretical EMF produced by the inductor can be found as follows:

𝑉𝐿 = 𝐿

I.

𝑑𝑖

𝑑

𝑡

𝑡

= 𝐿 (𝐼𝐹 [1 − 𝑒 − ⁄𝜏𝐿 ]) = 𝜀𝑒 − ⁄𝜏𝐿

𝑑𝑡

𝑑𝑡

Graphing Current vs Time (25 points)

Consider an RL circuit that is being charged with a voltage source ε. The voltage across the inductor is

shown as a function of time in the table below, with time in seconds (s) and voltage in volts (V). The

magnitude of the current a...