AC circuits with resistor/inductor/capacitor

anonymous613

Hi folks,

I am unable to answer the following questions. I know what the answers are (5 - b, 10 - b, 12 - c), but I do not know how those answers are explained. I am also unable to find any relationships in my textbook that explain the relationships expressed in these questions:

5. As the frequency ina simple ac circuit consisting of an alternating emf and a resistor increases, the rms current through the resistor (a)increases. (b) does not change. (c) may increase or decrease depending on the magnitude of the original frequency. (d) may increase or decrease depending on the magnitude of the resistance. (e) decreases.

10 ∙ If the frequency in the circuit shown in Figure 31-27 (consits of an AC emf connected to an inductor) is doubled, the inductance of the inductor will (a) increase by a factor of 2. (b) not change. (c) decrease by a factor of 2. (d) increase by a factor of 4. (e)
decrease by a factor of 4.

If the frequency in the circuit in Figure 31-28 (consists of an alternating emf connected to a capacitor) is doubled, the capacitative reactance of the circuit will (a)
increase by a factor of 2. (b) not change. (c) decrease by a factor of 2. (d) increase by a factor of 4. (e)
decrease by a factor of 4.

Thanks a lot for your help,
A

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arcnets

Welcome anonymous613,
I think the key to all this is the concept of 'impedance'. This is a generalization of 'resistance', and you need it when analyzing AC circuits. Resistors, inductors, and capacitors all have impedance. I suggest you look up this keyword in your textbook.

J-Man

(5) First some (simple and imprecise) definitions...
Current is simply the amount of charge per time that flows through a conductor.
Frequency is how fast the current changes direction.
RMS current is the Root-Mean-Square Current; this is basically an "average (mean) current" we first square the current, then take the average, then take the square root. Since we are first square and then square-rooting, that process basically cancels each other out, except for one important thing: the answer is always positive. This is useful for situations, such as AC current analysis, where half the current is negative and the other half positive.
Since the voltage is constant and the impedance is constant, the (average) current is constant; only the time it takes the current to go from positive to negative to positive is changing. Therefore the rms current stays the same.

(10) Adding a voltage/current or changing the frequency to a material doesn't change it's physical properties (more or less), that is why electronics works in the first place. You can't change the value of an inductor except by changing it material, changing how much of the material is used, changing the geometry of the material or adding so much energy that the material is destroyed. Of course, temperature does play a part.

(Unnumbered) Capacitance reactance is defined as Xc = 1/wC, where Xc is the reactance, w is the frequency and C is the capacitance. So if you multiply w by 2, you must divide Xc by 2.

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