Question

A fully charged capacitor with a voltage of 270 V is discharged through a resistor. (a) What is the voltage across the capacitor at the end of five time constants? (b) At this time, what is the voltage across the resistor?

Answer 1

a)

The time constant is the time required for the capacitor to discharge to a value of

1/e of its original charge, where e is a constant (the base of natural, or Napierian

logarithms, and numerically, e is irrational, equal to about 2.718281828459.)

The voltage across the capacitor is directly proportional to the charge on the

capacitor, and after 5 time constants it has decreased to 1/(e^5) of its fully

charged value of 270 V. If e equals 2.718281828..., e to the 5th power equals

148.41 (to 5 significant figures) so the voltage across the capacitor after 5 time

constants equals 270 volts divided by 148.41,

i.e:

= 270/148.41 = 1.82 V (ans)

b)

If the resistor is connected directly across the capacitor, the voltage across

the capacitor and resistor are the same at all times. i,e

= 1.82 V (ans)