A series RLC circuit is made with a C=100pF capacitor, an L=100μH inductor, and an R=30Ω resistor. The circuit is driven at 5×106rad/s with a 1V amplitude. What is the current oscillation amplitude in amps
Freq. = 5*10^6rad/s * 1rev/6.28rad =
7.958*10^5 rev/s = 7.958*10^5 Hz.
Xl = WL = (6.28*7.958*10^5)*100*10^-6 =
500 Ohms.
Xc=1/WC = 1/(6.28*7.958*10^5)*100*10^-12
= 2000 Ohms.
Z = R + j(Xl-Xc) = 30 + j(500-2000) =
30 - j1500 = 1500.3Ohms [-88.9o]
I = V/Z = 1.0[0o]/1500.3[-88.9] =
6.67*10^-4 Amps.
Hujhgs hhh
To find the current oscillation amplitude in amps, we can use the concept of impedance in an RLC circuit.
Impedance is the effective resistance offered by a circuit to an AC current. In an RLC circuit, the impedance is given by the equation:
Z = √(R^2 + (ωL - 1/(ωC))^2)
where Z is the impedance, R is the resistance, ω (omega) is the angular frequency of the AC current, L is the inductance, and C is the capacitance.
In this case, R = 30Ω, ω = 5×10^6 rad/s, L = 100μH = 100×10^(-6)H, and C = 100pF = 100×10^(-12)F.
Let's calculate the impedance:
Z = √(30^2 + (5×10^6 × 100×10^(-6) - 1/(5×10^6 × 100×10^(-12)))^2)
Simplifying,
Z = √(900 + (500 - 2000)^2)
Z = √(900 + 1500^2)
Z = √(900 + 2250000)
Z ≈ √2250900
Z ≈ 1503 Ω
Once we have the impedance, we can find the current (I) using Ohm's Law:
I = V/Z
where V is the voltage amplitude. In this case, V = 1V.
I = 1V / 1503 Ω
I ≈ 0.000665 A (or 665 μA)
Therefore, the current oscillation amplitude in amps is approximately 0.000665 A (or 665 μA).