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There are 2 different potential differences in this question. One is the PD along each strip in the direction of $l$ - ie horizontal. I shall call this $V_x$. The other is the PD between the 2 strips in the direction of $b$ - ie vertical - at the same horizontal position $x$. I shall call this $V_y$, but note that like $V_x$ it also depends on $x$.
Option D is asking for an expression for $V_y$.
If the current has reached a limiting constant value, which will happen after the battery has been connected for a long time, then the PD $V_x$ along each strip depends only on its resistance not its inductance, because there is no back emf in an inductor if the current through it is not changing. In this case the vertical PD between the strips increases linearly from $0$ to $V_0$ when measured from the RH end where they are shorted : $$V_y=V_0 \frac{x}{l}$$
Before the current becomes constant there is a potential drop $V_R=IR$ across each strip due to its resistance $R$. Initially $I$ is very small so $V_R=IR \ll \frac12 V_0$. At the same time there is a back emf of $V_L=L\frac{dI}{dt}$ while the current increases, where $L$ is inductance. This is also a potential drop across the inductor, and it is linear (proportional to $x$) because inductance $L$ like resistance $R$ is proportional to length. Initially $\frac{dI}{dt}$ is large and $V_L =L\frac{dI}{dt} \approx \frac12 V_0$.
The sum of these 2 PDs equals the PD supplied by the battery, the same as when there is a separate resistor and inductor in series : $$V_R+V_L=\frac12 V_0$$ So the total PD $V_x$ along each strip varies linearly even when the current is changing, and the PD $V_y$ between the 2 strips again increases linearly from the RH end, as in the above equation.
In a circuit, a capacitor (Xc=30Ω, R=44Ω) and an inductor (Xl=90Ω, R=36Ω) are connected in series with an AC source (ƒ=60Hz, V=200V). Determine:
1-current intensity
2-the voltage across every component in the circuit.
Homework Equations
Z=√R²+(Xl-Xc) Where: Z is the impedance, Xl is the inductive reactance, and Xc is the capacitive reactance.
I=V/Z
The Attempt at a Solution
That is how I solved the problem:
Could someone explain it for me?
Answers and Replies
cnh1995
This is how a lossy capacitor is represented:
Perhaps there is a mistake in the book's solution.
This is how a lossy capacitor is represented:
View attachment 112591But then Z is not 100 ohm as both the resistances are no longer in series.
Perhaps there is a mistake in the book's solution.
@Asmaa Mohammad is right to question the book's discrepancy in dealing with the resistance and reactance components differently for the two components. For the apparent course level I would be inclined to interpret the circuit as follows:
and to treat the capacitor and inductor in the same fashion mathematically.
Likes cnh1995
This is how a lossy capacitor is represented:
View attachment 112591But then Z is not 100 ohm as both the resistances are no longer in series.
Perhaps there is a mistake in the book's solution.
Gneill, still I don't know if my answer is correct or not?
@Asmaa Mohammad is right to question the book's discrepancy in dealing with the resistance and reactance components differently for the two components. For the apparent course level I would be inclined to interpret the circuit as follows:
and to treat the capacitor and inductor in the same fashion mathematically.
cnh1995
Gneill, still I don't know if my answer is correct or not?
Perhaps there is a mistake in the book's solution.
Gneill, still I don't know if my answer is correct or not?
When you submit your work for marking you might want to include a brief argument for not treating the resistance as separate components when judging the voltage across the "real" components.
Likes cnh1995
Their calculation of inductor voltage is correct and they should have taken the 44 ohm resistor in series with the capacitance
Ok, guys, is this answer correct?
I would say it is not correct. I feel that the components of the circuit are the non-ideal capacitor and inductor and that their internal resistance can't be separated as separate components. The textbook's approach for the inductor is valid and they have obtained a correct result for it. My advice is to do the same thing for the capacitor.
When you submit your work for marking you might want to include a brief argument for not treating the resistance as separate components when judging the voltage across the "real" components.
Likes gneill
Thank you, cnh1995!