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.
#12A (4 points possible)
What is the current oscillation amplitude in A?
What is the current oscillation amplitude in A? - unanswered
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#12B (3 points possible)
Which of the following will increase the current amplitude?
- unanswered increase the resistance increase the frequency decrease the capacitance decrease the inductance
Or else you're taking a test.
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To find the current oscillation amplitude in the given RLC circuit, we can use the formula for impedance in AC circuits and Ohm's Law.
The impedance of an RLC circuit is given by the equation:
Z = √(R^2 + (ωL - 1/(ωC))^2)
where Z is the impedance, R is the resistance, L is the inductance, C is the capacitance, and ω is the angular frequency.
In this case, the angular frequency is given as 5×10^6 rad/s. Let's substitute the given values into the equation:
Z = √(30^2 + (5×10^6 × 100×10^-6 - 1/(5×10^6 × 100×10^-12))^2)
Z = √(900 + (5 - 200)^2)
Z = √(900 + 3^2)
Z = √(900 + 9)
Z = √909
Z ≈ 30.149 Ω
Now, we can apply Ohm's Law to find the current oscillation amplitude:
V = I × Z
where V is the voltage amplitude (given as 1V) and I is the current amplitude.
1 = I × 30.149
I ≈ 1 / 30.149
I ≈ 0.033 A
Therefore, the current oscillation amplitude in the RLC circuit is approximately 0.033 A.
For the second question regarding increasing the current amplitude, let's consider the factors that affect the impedance of the circuit:
- Increase the resistance (R): Increasing the resistance value in the circuit will decrease the impedance, which will increase the current amplitude.
- Increase the frequency (ω): Increasing the angular frequency will increase the impedance, which will decrease the current amplitude.
- Decrease the capacitance (C): Decreasing the capacitance value will decrease the impedance, which will increase the current amplitude.
- Decrease the inductance (L): Decreasing the inductance value will increase the impedance, which will decrease the current amplitude.
Based on these observations, increasing the resistance or decreasing the capacitance will increase the current amplitude. Therefore, the correct answer is "increase the resistance" and "decrease the capacitance."