AS Level Timing >RC Timing< Schmitt NOT Astable 
Timing RC Timing 

In addition to the basic timing concepts needed for all subject levels, AS and A Level students need a more mathematical approach involving logarithmic and exponential maths. This involves the ln button on your calculator that you may not have used before. The inverse button function is the e^{x} exponential. Some calculators have separate buttons for these functions. You'll also need to learn the difference between the  button and the ± button. In everyday English you may have heard of exponential growth or decay. That's the e^{x} button on your calculator.
Formula 

Time Constant = R C 
Charging: T_{63%} = R C T_{50%} = 0.69 R C T_{100%} = 5 R C Discharging: T_{37%} = R C T_{50%} = 0.69 R C T_{0%} = 5 R C 555 Monostable: T_{66.6%} = 1.1 R C 
Charging Volts 
V_{C} = V_{0} ( 1  e^{  t / RC}) If you know the time, you can calculate the volts. 
Discharging Volts 
V_{C} = V_{0} e^{  t / RC} If you know the time, you can calculate the volts. 
Charging Time 
t = RC ln( 1  V_{C} / V_{0} ) If you know the volts, you can calculate the time. 
Discharging Time 
t = RC ln( V_{C} / V_{0} ) If you know the volts, you can calculate the time. 
For this circuit, the time constant T = R C = 1 x 10^{6} x 1 x 10^{6} = 1 Second
For an uncharged capacitor, after a time t, the capacitor voltage V_{C} = V_{0} ( 1  e^{  t / RC})
This is tricky to work out with a calculator. You could attempt it using loads of brackets.
Or you could break it down into smaller safer calculations.
Here is a test case. After 0.69 seconds, the circuit above should have charged to 50% of V_{0}. If V_{0} is 100 Volts, the answer should be very close to 50V.
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