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If you want to discharge a 3000 WVDC 0.75 µF capacitor to less than 1% of its charge in 15 seconds, what resistor should you choose?

Answer :

Final answer:

To discharge a 3000 WVDC 0.75 uF capacitor to less than 1% of its charge in 15 seconds, a resistor of 4 MΩ is required.

Explanation:

To determine the resistance needed to discharge a 3000 WVDC 0.75 uF capacitor to less than 1% of its charge in 15 seconds, we can use the RC time constant formula τ = RC, where τ (tau) is the time constant, R is the resistance, and C is the capacitance. The time constant τ is the time it takes for the voltage across the capacitor to fall to about 36.8% of its initial value. To discharge to less than 1%, we need approximately 5 time constants (since (0.368)^5 < 0.01).

First, calculate the total time to discharge to 1% of the initial charge: t = 5τ. So 5τ = 15 seconds, therefore τ = 15/5 = 3 seconds. Now incorporating the capacitance C = 0.75 uF (which is 0.75 x 10^-6 F), we can solve for R: τ = R * C, thus R = τ / C = 3 / (0.75 x 10^-6 F) = 4,000,000 ohms or 4 MΩ.

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