A 21.3 k resistor and a capacitor are connected inseries and then a 12.0 V poten

Question

A 21.3 k resistor and a capacitor are connected inseries and then a 12.0 V potential difference is suddenly appliedacross them. The potential difference across the capacitor rises to6.53 V in 1.19 µs. (a) Calculate the timeconstant of the circuit (ins). (b) Find the capacitance of thecapacitor in nanofarads. Thanks for the help! A 21.3 k resistor and a capacitor are connected inseries and then a 12.0 V potential difference is suddenly appliedacross them. The potential difference across the capacitor rises to6.53 V in 1.19 µs. (a) Calculate the timeconstant of the circuit (ins). (b) Find the capacitance of thecapacitor in nanofarads. Thanks for the help! Thanks for the help!

Explanation / Answer

     Resistance   R = 21.3k = 21.3 *10 3      voltage    V =12 V     voltage acrosscapacitor     V C = 6.53V      time t = 1.19 s = 1.19*10-6 s    a)    voltage acrosscapacitor                V C   = V ( 1 - e - t / )               6.53 = 12 ( 1 - e - (t / )                1 - e - (t / )   = 0.544                1 - 0.544 = e - (t / )                - t /      = -0.7853         time constant   = t / 0.7853                                   = 1.515 s b) time constant   = R C                      15.15 *10-5 s   = R C      capacitance of the capacitor C =    1.515 *s / R                                                       = 1.515 s / 21300                                                           = 0.711 p F

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