Determining Inductance of an L-R Circuit

In summary, to calculate the inductance of an inductor in an L-R circuit, one must first determine the time constant tau using the current measurements at a specific time (I_0 and I_1) and the time at which they are taken (t_1). The inductance can then be calculated using the formula L = R*t_1*ln(I_0/I_1).
  • #1
hokie1020
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Urgent HW help!

In this problem you will calculate the inductance of an inductor from a current measurement taken at a particular time. Consider the L-R circuit shown in the figure. Initially, the switch connects a resistor of resistance R and an inductor to a battery, and a current I_0 flows through the circuit. At time t=0, the switch is thrown open, removing the battery from the circuit. Suppose you measure that the current decays to I_1 at time t_1.
PART A
Determine the time constant tau of the circuit.
Express your answer in terms of t_1, I_1, and I_0. Recall that natural logarithms are entered as ln(x).

PART B
What is the inductance L of the inductor?
Express your answer in terms of R, I_0, I_1, and t_1.Please help!
I know tau=L/R but i don't know how all those other variables come into play and since I don't know what L equals either, so I am not sure what to substitute into the equation to figure it out
 
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  • #2
.A. The time constant tau of the circuit is given by tau = t_1*ln(I_0/I_1).B. The inductance L can be determined from the equation L = R*tau = R*t_1*ln(I_0/I_1).
 

FAQ: Determining Inductance of an L-R Circuit

What is an L-R circuit?

An L-R circuit is a type of electrical circuit that contains both an inductor (L) and a resistor (R). It is commonly used in electronics and electrical engineering for a variety of purposes, such as creating delays, filtering signals, and reducing electromagnetic interference.

How do you determine the inductance of an L-R circuit?

The inductance of an L-R circuit can be determined by measuring the voltage and current of the circuit and using the formula L = V/I, where L is the inductance, V is the voltage, and I is the current. This calculation is based on the relationship between voltage, current, and inductance in an L-R circuit known as Ohm's Law.

What is the unit of measurement for inductance?

The unit of measurement for inductance is the Henry (H). However, in practical applications, smaller units such as millihenries (mH) or microhenries (µH) are often used.

Can the inductance of an L-R circuit change?

Yes, the inductance of an L-R circuit can change depending on various factors such as the type of inductor used, the materials it is made of, and the frequency of the current passing through it. Additionally, inductance can also be altered by adding or removing components from the circuit.

What are some common applications of L-R circuits?

L-R circuits have many practical applications, including in power supplies, audio equipment, and electronic filters. They are also commonly used in radio frequency (RF) circuits and inductors are essential components in the functioning of motors and generators.

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