Final answer:
It would take approximately 5.258 seconds to discharge a 150 μF capacitor through a 350 Ω resistor down to 1.00% of its original voltage.
Step-by-step explanation:
The time required to discharge a capacitor through a resistor can be calculated using the formula for the RC time constant and the exponential decay function. Specifically, the voltage across a discharging capacitor as a function of time, V(t), is given by:
V(t) = V_0 × e^{-t/RC}
where:
- V_0 is the initial voltage,
- e is the base of the natural logarithm,
- t is the time in seconds,
- R is the resistance in ohms (Ω), and
- C is the capacitance in farads (F).
To find the time when the voltage is at 1.00% of its original value, we can rearrange the equation to solve for t:
t = -RC × ln(0.01)
For the given values, R = 350 Ω and C = 150 μF, we have:
t = -350 × 150×10^-6 × ln(0.01) ≈ 5.258 seconds
Therefore, it would take approximately 5.258 seconds to discharge the 150 μF capacitor through a 350 Ω resistor down to 1.00% of its original voltage.