Current across resistor and inductor

In summary, the current through a resistor and inductor in series can be calculated using Ohm's Law if the voltage and inductive reactance are known. For the total current, use I = VS / (R + XL). For the current through the inductor, use I = VL / XL.
  • #1
verbose

Homework Statement


I have a resistor and an inductor in series. The current across each is the same, correct? I want to know if I can use Ohm's Law to solve for current across the inductor if I know the Voltage and inductive reactance. Basically, does I = V/X_{L} ?


Homework Equations



V = IR
I = V/R

does I = V/ X_{L} ?

The Attempt at a Solution

 
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  • #2
??What do you mean by X_{L}? I can guess that V is the voltage drop, I the current and R the resistance. Is X_{L} the inductance? If so then, no, the voltage drop over an inductance is NOT given by the same equation as for a resistance. Surely you have that formula in your text?
 
  • #3
X_{l}

by this i mean inductive reactance...sorry, it's tex syntax for X with L as a subscript. i have the habit of writing all my mathy stuff in latex syntax
 
  • #4
verbose said:
by this i mean inductive reactance...sorry, it's tex syntax for X with L as a subscript. i have the habit of writing all my mathy stuff in latex syntax
Yes, [tex]I = \frac{V_L}{X_L}[/tex]
Notice that [tex]X_L[/tex] is dependent of the frequency of [tex]V_L[/tex]
 
  • #5
verbose said:

Homework Statement


I have a resistor and an inductor in series. The current across each is the same, correct? I want to know if I can use Ohm's Law to solve for current across the inductor if I know the Voltage and inductive reactance. Basically, does I = V/X_{L} ?


Homework Equations



V = IR
I = V/R

does I = V/ X_{L} ?

The Attempt at a Solution


Forget the problem for a minute, first let's clear up that current isn't across anything. Current flows through and voltage is established across. Like fingers on a chalk board.:cry:
 
  • #6
If those 2 elements are in series (the resistor and inductor) and connected to a voltage source, the current through all elements will be given by:

I = VS / (R + XL)


If the voltage you are talking about is the voltage across the inductor, then yes, the current through all elements will given by:

I = VL / XL
 

1. What is the difference between current across a resistor and a current across an inductor?

The main difference between the current across a resistor and a current across an inductor is how they respond to changes in voltage. A resistor allows current to flow easily, while an inductor resists changes in current. This means that the current across a resistor will be proportional to the voltage, while the current across an inductor will lag behind the voltage.

2. How does the current across a resistor and an inductor affect the overall circuit?

The current across a resistor and an inductor affect the overall circuit by creating a phase difference between the voltage and current. This can cause the circuit to behave differently, depending on the values of the resistor and inductor. In some cases, the inductor can also store energy and release it back into the circuit, impacting the overall behavior.

3. How do I calculate the current across a resistor and an inductor in a circuit?

To calculate the current across a resistor, you can use Ohm's Law (I = V/R), where I is the current, V is the voltage, and R is the resistance. For an inductor, you can use the formula V = L di/dt, where V is the voltage, L is the inductance, and di/dt is the rate of change of current. You can then use these values to determine the current across each component in the circuit.

4. Can the current across a resistor and an inductor ever be equal?

Yes, under certain conditions, the current across a resistor and an inductor can be equal. This can happen when the inductor is in a steady state or if the frequency of the voltage source is high enough that the inductor's reactance is small. In this case, the inductor behaves more like a wire and the current across it can be equal to the current across the resistor.

5. How does the phase difference between the current across a resistor and an inductor change with frequency?

The phase difference between the current across a resistor and an inductor changes with frequency because the inductor's reactance (which is frequency-dependent) affects how it responds to changes in current. At low frequencies, the inductor's reactance is high, causing the current to lag behind the voltage. As the frequency increases, the reactance decreases and the current approaches the same phase as the voltage. At very high frequencies, the reactance becomes negligible and the current and voltage are in phase.

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