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AS Level     Timing     >RC Timing<     Schmitt NOT Astable    

Timing RC Timing


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  AS Level    RC Timing   0 of 3    Question 6    RC Time Constant 
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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 ex 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 ex button on your calculator.

Calculator_Ln_Button.jpg

 

Formula

Time Constant = R C

    Charging:             T63%   =   R C        T50%   =   0.69 R C        T100%   =   5 R C

    Discharging:         T37%   =   R C        T50%   =   0.69 R C        T0%   =   5 R C

    555 Monostable:   T66.6% =   1.1 R C

Charging Volts

    VC   =   V0 ( 1 - e - t / RC)    If you know the time, you can calculate the volts.

Discharging Volts

    VC   =   V0 e - t / RC    If you know the time, you can calculate the volts.

Charging Time

    t = -RC ln( 1 - VC / V0 )    If you know the volts, you can calculate the time.

Discharging Time

    t = -RC ln( VC / V0 )    If you know the volts, you can calculate the time.

RC Timing Circuit

Resistor Capacitor R C Timing

For this circuit, the time constant   T   =   R C   =   1 x 106 x 1 x 10-6   =   1 Second

For an uncharged capacitor, after a time t, the capacitor voltage   VC   =   V0 ( 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.

  1. Work out   t / (R C)
  2. Work out   e-( answer from step 1 )
  3. Work out   1   -   (answer from step 2)
  4. Work out   V0   x   (answer from step 3)

Here is a test case. After 0.69 seconds, the circuit above should have charged to 50% of V0. If V0 is 100 Volts, the answer should be very close to 50V.

  1. Work out   t / (R C)   =   0.69 / ( 1 x 1 ) because the Megohm 106 cancels out with the microfarad 10-6   =   0.69.
  2. Work out   e-( answer from step 1 )   =   e -0.69   =   0.502
  3. Work out   1   -   (answer from step 2)   =   1 - 0.502   =   0.498
  4. Work out   V0   x   (answer from step 3)   =   49.8 Volts   Very close to the expected answer - less than 1% out.

New Calculator Skills Video

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