Find current at high/low frequency

In summary: Ztot = Zl = jXl, and for b) Ztot = R + Zl = R + jXlIn summary, for a 45v (rms) power supply, the rms current delivered is 225mA when the frequency is very large and 450mA when the frequency is very small. This is due to the approximation that the impedance of the inductor and capacitor becomes infinite, eliminating one of the two loops in the circuit. The total resistance for these cases is equal to the resistance of the inductor in the first case and the resistance of the inductor plus the resistance of the resistor in the second case.
  • #1
Acuben
64
0

Homework Statement


find the rms current delievered by the 45v (rms) power supply when
a) the frequency is very large
and b) the frequency is very small.

answer: a) 225mA, b) 450mA

http://yfrog.com/jucurrentqg

http://img714.imageshack.us/img714/1592/currentq.gif

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Homework Equations


w= angular velocity (supposed to be omega)
L= inductor
C= capacitor
j= complex coefficent = sqrt(-1)
Zl= resistance of inductor
Zc= resistance of capacitor
Ztot= total resistance
R= resistance of resistor
P= Power

Xl=wL
Xc=1/wc
Zl=j*Xl
Zc=-j*Xc
Ztot= R + Zl + Zc = R + j(Xl-Xc)



The Attempt at a Solution



with frequency just being high, how am I supposed to get these exact numbers without letters/symbol for I? o.o I tried the calculation and omega did not cancel out either.
 
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  • #2
The key idea is that in the case of very high or very low frequency, you can take the impedance (resistance) of the inductor and capacitor to be ~infinite, respectively. Does it make sense why that's true (as an approximation at least)?

In effect, this eliminates one of the two loops in the circuit for each case.
 
  • #3
zhermes said:
The key idea is that in the case of very high or very low frequency, you can take the impedance (resistance) of the inductor and capacitor to be ~infinite, respectively. Does it make sense why that's true (as an approximation at least)?

In effect, this eliminates one of the two loops in the circuit for each case.

ah yes it does, at first I thought the resistance would skyrocket to infinity / 0
thank you
 
Last edited:

1. What is the difference between high frequency and low frequency currents?

High frequency currents refer to electrical currents that oscillate at a rate of more than 10,000 cycles per second, while low frequency currents oscillate at a rate of less than 10,000 cycles per second. In general, high frequency currents are used for more sensitive and precise applications, while low frequency currents are used for more general purposes.

2. How do you measure current at high and low frequencies?

To measure current at high and low frequencies, you will need a specialized instrument called an oscilloscope. This device measures the amplitude and frequency of an electrical signal and displays it on a screen. By connecting the oscilloscope to the circuit, you can measure the current at different frequencies and analyze its characteristics.

3. What are the applications of high frequency currents?

High frequency currents have a wide range of applications in various industries. Some of the most common uses include telecommunications, radio broadcasting, medical imaging, and high-speed data transmission. They are also used in scientific research for experiments involving electromagnetic fields and radiation.

4. How does current behave at high and low frequencies?

At high frequencies, current tends to flow along the surface of a conductor rather than through its entire cross-section. This is known as the skin effect, and it increases the resistance of the conductor. At low frequencies, current flows more evenly through the conductor, but its behavior can still be affected by other factors such as inductance and capacitance.

5. What factors affect the amount of current at high and low frequencies?

Several factors can affect the amount of current at high and low frequencies. These include the impedance of the circuit, the type of conductor and its material, the frequency of the current, and the surrounding environment. For high frequency currents, the skin effect and other electromagnetic phenomena also play a significant role in determining the amount of current.

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