When A 0.015-microfarad capacitor is charged to 25 volts. What is the voltage 25 milliseconds after placing a 2-megohm resistor across its terminals?

To find the voltage across the capacitor after 25 milliseconds when a 2-megohm resistor is placed across it, we can use the formula for the voltage across a discharging capacitor:

[ V(t) = V_0 \cdot e^{-\frac{t}{RC}} ]

where ( V_0 ) is the initial voltage (25 volts), ( R ) is the resistance (2,000,000 ohms), and ( C ) is the capacitance (0.015 microfarads or ( 0.015 \times 10^{-6} ) farads).

Calculating ( RC ) gives ( RC = 2,000,000 \times 0.015 \times 10^{-6} = 0.03 ) seconds. Thus, after 25 milliseconds (0.025 seconds):

[ V(0.025) = 25 \cdot e^{-\frac{0.025}{0.03}} \approx 25 \cdot e^{-0.8333} \approx 25 \cdot 0.4358 \approx 10.895 \text{ volts} ]

So, the voltage after 25 milliseconds is approximately 10.9 volts.