A friend working on a psychology experiment asks you for help with the design of a simple circuit. She needs an LC timing circuit in which the voltage on a fully charged capacitor drops to zero in 15s . She has a 20H inductor available, but doesn't know what value of capacitor to use. What do you recommend?
The period of charge oscillation will be
P = 2*pi*sqrt(L*C)
In time P/4 , capacitor charge will fall to zero.
To design the LC timing circuit, you will need to calculate the value of the capacitor based on the given information.
The time it takes for the voltage on a fully charged capacitor to drop to zero in an LC circuit is given by the formula:
t = 1 / (2π√LC)
Given: t = 15s, L = 20H
To find the value of C, we can rearrange the formula:
C = 1 / (4π²Lt²)
Substituting the given values:
C = 1 / (4π² * 20 * (15²))
C = 1 / (4π² * 20 * 225)
C ≈ 0.000004456 F
Therefore, I would recommend using a capacitor with a value of approximately 0.000004456 F to achieve a voltage drop to zero in 15s when paired with the 20H inductor.
To recommend a suitable value of capacitor for the LC timing circuit, we need to understand the behavior of an LC circuit and its time constant.
Here's how you can help your friend determine the value of the capacitor:
Step 1: Understand the behavior of an LC circuit:
An LC circuit consists of an inductor (L) and a capacitor (C) connected in series or parallel. When the circuit is energized, the energy oscillates back and forth between the inductor and the capacitor. The voltage across the capacitor increases as energy is stored in it and decreases as energy is transferred to the inductor.
Step 2: Determine the time constant of the LC circuit:
The time constant (τ) of an LC circuit can be calculated using the formula:
τ = L / R
where L is the inductance (20H in this case).
Step 3: Determine the desired voltage drop time:
Your friend needs the voltage on the fully charged capacitor to drop to zero in 15 seconds.
Step 4: Calculate the capacitance using the time constant:
To find the capacitance (C), use the formula:
τ = RC, rearranged to C = τ / R
In this case, τ = 15s (desired voltage drop time), and R is the equivalent resistance of the circuit (which should be as high as possible to avoid significant energy loss).
In this scenario, we assume the resistance of the circuit is negligible, so we can disregard it for simplicity and focus on finding the value of capacitance (C).
C = τ / R
C = 15s / R
Step 5: Determine a suitable value for R:
Since your friend wants a fully charged capacitor to drop to zero in 15 seconds, R should be as high as possible to reduce energy loss and maintain a higher voltage.
In practical terms, a suitable value for R could be on the order of tens or hundreds of kilohms, depending on the specific requirements of the circuit. Your friend can choose a resistor value that is readily available and meets the experimental requirements.
With these steps completed, you can now recommend a suitable value of capacitance (C) once your friend determines the desired resistance (R) for the circuit.