AS Level    RC Timing     Questions 0 to 3   -->  View All  

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.

RC Timing Circuit

• The power supply voltage is V₀
• The capacitor voltage is V_C
• The elapsed time is t.

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   V_C   =   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