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A circuit contains a 20 ohm resistor and an inductor with an inductance of 0.093 H if the circuit has a frequency of 60Hz what is the total impedance of the circuit?
Wiki User
∙ 14y ago
The expression for the current (I) is simply the voltage (V) divided by the total impedance (Z).
In your example its (40+j25) V divided by (R + / - j) Ohms.
We aren't given the dc resistance of the inductor so assuming it is zero.
Resistance of resistor is 20 Ohms.
Reactance of inductor is 2 * Pi * Freq * Inductor value in Henries. gives
2*3.14*79.5*0.6 = 299.7 Ohms.
So total impedance Z is (20+j299.6) Ohms....say (20+j300) Ohms
Now Complex series current I = V/Z = (40+j25) V / (20+j300) Ohms
Rather than taking surds we simplify to polar form here.
V = (40+j25) = 47.17 Volts at phase angle 32 degrees
Z = (20+j300) = 300.7 Ohms at phase angle 86.2 degrees
So current is 47.17 V /300.7 Ohms and phase angle is (32 degrees - 86.2 degrees)
I = 0.157 Amps at angle -54.2 degrees
Changing this to rectangular form gives (0.092 -j0.127) Amps
Wiki User
∙ 11y ago
Wiki User
∙ 14y agoThe impedance of the coil is [ 2pi f L ]j = [ 2pi 60 0.093 ]j = j36.06 ohms.
The question doesn't tell us whether the components are in series or parallel.
If in series: The total impedance is their sum = [ 20 + j36.06 ] ohms.
Magnitude = 41.235, Angle = 61 degrees.
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If in parallel ... I'm not sure I can do this ... the total impedance is (their product) divided by (their sum).
(20 x j36.06) / (20 + j36.06)
= (20 x j36.06) x (20 - j36.06) / [ (20 + j36.06) x (20 - j36.06) ]
= j721.2 x (20 - j36.06) / (400 + 1,300.32)
= (j14,424 + 26,006.47) / (1,700.32)
= [ 15.295 + j8.483 ] ohms
Magnitude = 17.49, Angle = 29 degrees.
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If these results are wrong, at least I tried without giving up.
If they're correct ... I'll admit it, I'm not proud ... I expect a trust point for going through this aggravation and heartburn !
OMG ! Look at that ! The sum of the angles of the series and parallel impedances is 90 degrees !
That has to mean something I'll betcha !
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What is the impedance of an 8 Henry inductor at 120 Hz?
Use the formula: reactance equals 2.pi times frequency times inductance.
In an AC circuit with only an inductor what will an increase in frequency do?
Inductor impedance is given by jwL, where w=2*pi*frequency. Therefore as the frequency increases the impedance of the inductor increases, causing a larger current flow and a larger power dissipation across the inductor
Why the current increases upto resenance frequency and decreases there after in a series LCR circuit?
At resonance, the L and C impedance cancels out, so the current can be calculated based on the resistance and applied voltage. Imagine increasing frequency of the supply from 0 Hz to very high. At low frequency, the impedance of the inductor is ~0 (defined as Zl = w*L*j), and the impedance of the capacitor is very large (defined as Zc = 1 / (w*C*j)). As you increase the frequency, the impedance of the capacitor will decrease, as the impedance of the inductor increases. At some point (the resonant frequency), these two will be equal, with opposite signs. After crossing the resonant frequency, the inductor impedance will continue growing larger than the capacitor impedance until the total impedance approaches infinite.
Contains both resistance and inductance?
Wire. conductors. Wire made into a coil, an inductor.
What is resonance frequency in electronics?
The frequency at which the impedance of the circuit becomes zero is known as resonance frequency. Actually at resonance resistance only presence in the circuit. That means the impedance of the inductor and capacitor will automatically vanish.
How component size decreases when frequency decreases?
The impedance of a component (inductor or capacitor) will change with frequency - resistor impedances will not. Inductor impedance - j*w*L Capacitor impedance - 1/(j*w*C) L = inductance, C = capacitance, j = i = imaginary number, w = frequency in radians The actual inductance and capacitance does not change with frequency, only the impedance.
Why does the inductance of inductor varies with frequency?
It doesn't. the impedance of the inductor will, following the rule j*w*l, where l is inductance, w is frequency in radians and j is the imaginary number designating this a reactance, not resistance.
What is the impedance of an 8 Henry inductor at 120 Hz?
Use the formula: reactance equals 2.pi times frequency times inductance.
In an AC circuit with only an inductor what will an increase in frequency do?
Inductor impedance is given by jwL, where w=2*pi*frequency. Therefore as the frequency increases the impedance of the inductor increases, causing a larger current flow and a larger power dissipation across the inductor
What is inductance and capacitance and impedence?
The inductance of an inductor is the capacity of the inductor to induce electric flux. The capacitance of a capacitor is the capacity of the capacitor to store charges. THE IMPEDANCE OF A CIRCUIT IS THE TOTAL OPPOSITION OFFERED TO THE FLOW OF ELECTRIC CURRENT.
Does the impedance of a parallel RLC circuit equal to the value of the resistor?
No. You have to consider the inductor and the capacitor. Impedance of RLC circuit is equal to to the Value of Resistor Only AND Only on Resonate frequency. otherwise u have to cnsider resistance inductance and capacitance together in series.
How do you increase the inductance in a inductor?
Since we know that inductance of an inductor depends on the length of inductor by the formula L=muAN*N/l, where l is the length of inductor. So by varying the length of inductor we say that inductance of inductor varies.
What does a resonators do in a electric circuit?
A resonator is a circuit that responds to a narrow range of frequencies. A typical resonator is a tuned circuit containing an inductor and a capacitor in series or parallel. A series connected tuned circuit has zero impedance at the resonant frequency, while a parallel tuned circuit has infinite impedance at the resonant frequency. The resonant frequency in both cases depends on the inductance times the capacitance: F = 1 / (2.pi.sqrt(LC)) If the inductance is in Henrys and the capacitance in Farads, the answer is in Hz.
Why the current increases upto resenance frequency and decreases there after in a series LCR circuit?
At resonance, the L and C impedance cancels out, so the current can be calculated based on the resistance and applied voltage. Imagine increasing frequency of the supply from 0 Hz to very high. At low frequency, the impedance of the inductor is ~0 (defined as Zl = w*L*j), and the impedance of the capacitor is very large (defined as Zc = 1 / (w*C*j)). As you increase the frequency, the impedance of the capacitor will decrease, as the impedance of the inductor increases. At some point (the resonant frequency), these two will be equal, with opposite signs. After crossing the resonant frequency, the inductor impedance will continue growing larger than the capacitor impedance until the total impedance approaches infinite.
What is working principle of inductor?
A changing current through an inductor induces a voltage into the inductor, the direction of which always opposes the change in that current.So, in a d.c. circuit, an inductor will oppose (not prevent) any rise or fall in current, although the magnitude of that current will be determined by the resistance of that inductor, not by its inductance.In an a.c. circuit, because the current is continuously changing both in magnitude and in direction, it acts to continuously oppose the current due to its inductive reactance. Inductive reactance is proportional to the inductance of the inductor and the frequency of the supply. The vector sum of the inductive reactance of the inductor and the resistance of the inductor, is termed the impedance of the inductor. Inductive reactance, resistance, and impedance are each measured in ohms.
Contains both resistance and inductance?
Wire. conductors. Wire made into a coil, an inductor.
What is resonance frequency in electronics?
The frequency at which the impedance of the circuit becomes zero is known as resonance frequency. Actually at resonance resistance only presence in the circuit. That means the impedance of the inductor and capacitor will automatically vanish.
