How Do You Solve Complex Electrical Circuit Problems?

[Pepsi24chevy]

They go as followed:
1. A 30.0 mH inductor is connected to a standard electrical outlet (Vrms = 120 V; f = 60.0 Hz). Determine the energy stored in the inductor at t = (1/170) s, assuming that this energy is zero at t = 0.

2. What is the maximum current in a 5.00 µF capacitor when it is connected across a North American electrical outlet having Vrms = 120 V, f = 60.0 Hz?
mA
(b) What is the maximum current when it is connected across a European electrical outlet having Vrms = 240 V and f = 50.0 Hz?
mA

3. A sinusoidal voltage V(t) = (40.0 V) sin(100t) is applied to a series RLC circuit with L = 150 mH, C = 99.0 µF, and R = 83.0 .
(a) What is the impedance of the circuit?

(b) What is the maximum current?
A
(c) Determine the numerical values for Imax, , and in the equation i(t) = Imax sin( t - ).Imax = A
= rad/s
= °



4. Suppose you manage a factory that uses many electric motors. The motors create a large inductive load to the electric power line, as well as a resistive load. The electric company builds an extra-heavy distribution line to supply you with a component of current that is 90° out of phase with the voltage, as well as with current in phase with the voltage. The electric company charges you an extra fee for "reactive volt-amps" in addition to the amount you pay for the energy you use. You can avoid the extra fee by installing a capacitor between the power line and your factory. The following problem models this solution.
In an LR circuit, a 120 V (rms), 60.0 Hz source is in series with a 20.0 mH inductor and a 16.0 resistor.

(a) What is the rms current?
A
(b) What is the power factor?

(c) What capacitor must be added in series to make the power factor 1?
µF
(d) To what value can the supply voltage be reduced if the power supplied is to be the same as before the capacitor was installed?
V


5. series RLC circuit has components with following values. L = 20.0 mH, C = 100 nF, R = 10.0 , and Vmax = 100 V, with V = Vmax sin t. Find the following quantities.
(a) the resonant frequency
kHz
(b) the amplitude of the current at the resonant frequency
A
(c) the Q of the circuit

(d) the amplitude of the voltage across the inductor at resonance
kV


6. The RC low-pass filter shown in Figure 33.26 has a resistance R = 90.0 and a capacitance C = 8.00 nF. Calculate the ratio (Vout/Vin) for the following input frequencies.

Figure 33.26 http://www.webassign.net/pse/33-23.gif

(a) 680 Hz

(b) 680 kHz


7.An 80.0 resistor, a 170 mH inductor, and a 0.130 µF capacitor are connected in parallel across a 120 V (rms) source operating at 374 rad/s.
(a) What is the resonant frequency of the circuit?
Hz
(b) Calculate the rms current in the resistor, the inductor, and the capacitor.
IR = A
IL = A
IC = mA
(c) What rms current is delivered by the source?
A
(d) Is the current leading or lagging behind the voltage? By what angle?
°


ANy help in setting these up would be greatly appreciated!

 

[Päällikkö]

https://www.physicsforums.com/showthread.php?t=4825

 

[Pepsi24chevy]

well for 1, i gto Vmax =sqrt2 *120. Then i used I max = (Vmax/wL) a then i substitued into i(t) = imaxsin wt then i did Ul= 1/2Li^2 and i got .005 but i am pretty sure this isn't correct.

for 2 i did Xc= 1/(5e-6*60*2pi) then i did 120/530 and got .226 but I don't believe that is correct.

for 3 i figured most of it out.
a) What is the impedance of the circuit?
119
(b) What is the maximum current?
A.336
(c) Determine the numerical values for Imax, , and in the equation i(t) = Imax sin( t - ).Imax =
I got theto to equal -46. I got imax to be 33.96 because i did .336* each one of the resistance and took the highest value but it says that part is wrong.

for 4, I tried to follow the steps i did in 3 and i used1/w^2L to find the capacitance and then divided the amps i found by sqrt(2) but it didnt' work out as i got 4.8 for my answer which seems too high.

well i have to get to class, but this is what work i have for these problems, i have some more work on the other ones, but i dont' have time to ttype it. My fault earlier for not posting what work i have.