- #1
Oren Becker
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Hello.
I am taking a first year electricity and magnetism course.
In class, the following was taught:
a. What is the impedance of an inductor?
b. What is the total impedance of 2 components connected serially?
But only at home I realized that I don't understand some of the derivation.
Vp - Voltage at peak.
L - Inductance.
w - angular frequency
theta - phase
I was able to derive the impedance of a resistor and a capacitor using phasors.
I had a problem with the derviation for an inductor:
dI/dt = (Vp/L) * exp(j * (wt - theta))
At this point the professor integrated both sides, but did not add a constant of integration. As much as I understand, this is equivalent to the assumption that when the voltage is zero, the current is also zero. Is this assumption really necessary and what is its justification?
Regarding 2 components connected serially:
We where told this is analogous to resistance and resistors. Trying to understand this, I wrote:
V1 + V2 = V = Vp * exp(j * (wt - theta))
I1 = I2 = I
Therefore: Vp * exp(j * (wt - theta)) = V = Z1*I + Z2*I = (Z1 + Z2) * I
which implies that the total impedance really is Z1+Z2.
But the whole concept of impedance was developed assuming that the voltage across the component looks like: Vp * sin(wt - theta). But here, all the information I have is that the sum of the voltages is in that form. I don't see why each of them is of that form, and therefore I don't understand the justification for this derivation.
Thanks in advance for your help,
Oren.
Homework Statement
I am taking a first year electricity and magnetism course.
In class, the following was taught:
a. What is the impedance of an inductor?
b. What is the total impedance of 2 components connected serially?
But only at home I realized that I don't understand some of the derivation.
Homework Equations
Vp - Voltage at peak.
L - Inductance.
w - angular frequency
theta - phase
The Attempt at a Solution
I was able to derive the impedance of a resistor and a capacitor using phasors.
I had a problem with the derviation for an inductor:
dI/dt = (Vp/L) * exp(j * (wt - theta))
At this point the professor integrated both sides, but did not add a constant of integration. As much as I understand, this is equivalent to the assumption that when the voltage is zero, the current is also zero. Is this assumption really necessary and what is its justification?
Regarding 2 components connected serially:
We where told this is analogous to resistance and resistors. Trying to understand this, I wrote:
V1 + V2 = V = Vp * exp(j * (wt - theta))
I1 = I2 = I
Therefore: Vp * exp(j * (wt - theta)) = V = Z1*I + Z2*I = (Z1 + Z2) * I
which implies that the total impedance really is Z1+Z2.
But the whole concept of impedance was developed assuming that the voltage across the component looks like: Vp * sin(wt - theta). But here, all the information I have is that the sum of the voltages is in that form. I don't see why each of them is of that form, and therefore I don't understand the justification for this derivation.
Thanks in advance for your help,
Oren.