How long would it take to discharge a 0.026 microFarad capacitor to 6.4 % of its full charge through a resistance of 1.7 MOhm?
To determine how long it would take to discharge a capacitor to a specific percentage of its full charge, we can use the formula for exponential decay in an RC circuit:
V(t) = V(0) * e^(-t/RC)
Where:
- V(t) is the voltage across the capacitor at time t
- V(0) is the initial voltage across the capacitor
- t is the time
- R is the resistance in the circuit
- C is the capacitance of the capacitor
We're given the initial voltage (V(0)) and the capacitance (C), but we need to find the time (t) at which the voltage across the capacitor is 6.4% of V(0).
First, let's rewrite the formula to solve for time, t:
t = -RC * ln(V/V(0))
Where:
- ln is the natural logarithm function
- V is the voltage across the capacitor at time t
Now, we can plug in the given values:
V = 0.064 * V(0) (6.4% of full charge)
R = 1.7 MOhm (1.7 * 10^6 Ohm)
C = 0.026 microFarad (0.026 * 10^(-6) Farad)
Substituting these values into the formula:
t = - (1.7 * 10^6 Ohm) * (0.026 * 10^(-6) Farad) * ln(0.064)
Now, we can simplify and calculate the time, t, using a scientific calculator or a computer program:
t = - (1.7 * 10^6) * (0.026 * 10^(-6)) * ln(0.064)
t ≈ -44.742 seconds
Since time cannot be negative in this context, the absolute value gives the time it takes to discharge the capacitor:
t ≈ 44.742 seconds
Therefore, it would take approximately 44.742 seconds to discharge the 0.026 microFarad capacitor to 6.4% of its full charge through a resistance of 1.7 MOhm.