Inductor voltages and currents

In summary: No, current does not HAVE to flow to the negative side of a voltage source in such idealized problems.
  • #1
Homework Statement
a. What is the energizing circuit time constant?
b. Close the switch and determine the equation for iL and vL during current buildup.
c. What are iL and vL at t = 25 ms?
Relevant Equations
i = E/R*(1 - e^{-Rt/L})

I have redrawn the circuit as below

40 - (I2+0.5)200 - (I2 + IL)*300 = 0 -> eq1
-(I2 + IL)*300 - IL*280 - 4*dIL/dt = 0 -> eq2
Are my equations correct?
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  • #2
Looks good to me.
  • #3
I tried the following but answer does not match

##40 - (I_2 + 0.5)200 - (I_2+I_l)*300=0 ## -> 1
##500i_2 = 140 - 300i_l ## -> 1i
##-(I_2+I_l)*300 - I_l*280 - 4\frac{dI_l} {dt} =0 ## -> 2
##-300I_2 - 580I_l - 4 \frac{dI_l} {dt} = 0 ## -> 2i
Substituting 2i in 1i
##\frac{di_l} {dt} + 75i_l + 21 =0 ## Solving for il
##i_l = \frac{21e^{-75t}} {75} - \frac{21} {75} ##
a. Energizing circuit time out, i tried to calculate ##\tau##
##\tau = \frac{1} {75} = 0.013## But the answer is 10ms.
  • #4
There's a sign error when you put the numbers into eqn 1.

edit: BTW, this kind of mistake is incredibly common when doing this sort of problem. We ALL do it, all the time. You should just get used to checking for them. It's tedious, but the effort saved by avoiding confusion is worth it in the long run.
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  • #5
Yes, i got the equation as
##i_l = \frac 9 {100}(1- e^{-100t})##Amps
##v_l = 36e^{-100t}##
The time constant is 10ms.
At 25ms
##i_l=82.6 A## ##v_l = 2.95V##

But one question that i want to understand is the negative of the voltage source is not ground reference. As per the theory the ground is low resistance path so the current will try to flow to the ground or negative side of the battery?
  • #6
"Ground" can be thought of as an arbitrary choice for the name of a circuit node. The analysis of this schematic is the same regardless of where you define ground to be. When you were figuring out KVL around each of those loops, did ground matter for your resulting equations?

Ground may not always be "the low resistance path", it is usually just a name. Ground really can matter if you are dealing with circuits that interface with other circuits, then "ground" may be a shared node between circuits.
  • #7
PhysicsTest said:
the current will try to flow to the ground or negative side of the battery?
In addition to @DaveE's explanation, keep in mind that current does not HAVE to flow to the negative side of a voltage source in such idealized problems. In real life you have issues in trying to swamp a battery or power supply with reverse current but in idealized beginner's problem, that is not the case. I'm NOT suggesting that it's happening in this case, I'm just pointing it out for completeness sake.

1. What is an inductor and how does it work?

An inductor is a passive electronic component that stores energy in the form of a magnetic field. It consists of a coil of wire that creates a magnetic field when an electric current flows through it. The strength of the magnetic field is directly proportional to the amount of current passing through the inductor. When the current changes, the magnetic field also changes, which induces a voltage in the inductor according to Faraday's law of induction.

2. What is the relationship between inductor voltage and current?

The relationship between inductor voltage and current can be described by Ohm's law for inductors, which states that the voltage across an inductor is equal to the inductance multiplied by the rate of change of current. In other words, the voltage across an inductor is directly proportional to the rate of change of current. This means that if the current through an inductor changes rapidly, the voltage across it will be high, and if the current changes slowly, the voltage will be low.

3. How does an inductor affect AC and DC circuits differently?

In an AC circuit, the current is constantly changing direction, which means that the magnetic field in an inductor is also constantly changing. This results in an alternating voltage across the inductor. In a DC circuit, the current is constant, so the magnetic field in the inductor remains constant, resulting in no voltage across the inductor. However, when the current is first applied to a DC circuit, there is a brief period where the current is changing, which results in a temporary voltage across the inductor.

4. How does the value of inductance affect the behavior of an inductor?

The value of inductance determines the strength of the magnetic field created by the inductor for a given current. This means that a higher inductance value will result in a stronger magnetic field and therefore a higher voltage induced in the inductor. Additionally, a higher inductance value will cause the inductor to resist changes in current more, resulting in a longer time for the current to reach its maximum value.

5. What are some common applications of inductors?

Inductors are commonly used in electronic circuits for a variety of purposes, including filtering, energy storage, and timing. They are also used in power supplies to smooth out fluctuations in current and voltage. Inductors are also found in many electronic devices such as televisions, radios, and computers, where they are used in conjunction with capacitors to create tuned circuits for receiving and transmitting signals.

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