A charged capacitor is connected to a resistor and a switch asin Active Figure 1

Question

A charged capacitor is connected to a resistor and a switch asin Active Figure 18.17. The circuit has a time constant of 1.5 s.after the switch is closed, the charge on the capacitor is 75% ofits initial charge. (a) Find the time it takes to reach thischarge. (b) If R = 250 k, what is the value ofC. A charged capacitor is connected to a resistor and a switch asin Active Figure 18.17. The circuit has a time constant of 1.5 s.after the switch is closed, the charge on the capacitor is 75% ofits initial charge. (a) Find the time it takes to reach thischarge. (b) If R = 250 k, what is the value ofC.

Explanation / Answer

   Discharge of a capacitor is governed byequation    Q   =   Q0* e-t/CR    a.   given   CR   =   1.5s       Q   =   75%*Q0      =   0.75* Q0    0.75 *Q0   =   Q0 *e-t/1.5    0.75   =   e-t/1.5       et/1.5   =   1/0.75   =   1.33    t/1.5   =   ln1.33   =   0.2877    time   t   =   1.5* 0.2877   =   0.431   s    b.   CR   =   1.5   s          C   =   1.5/ R   =   1.5 / 250 *103      =   6.0*10-6   F   =   6.0   F       et/1.5   =   1/0.75   =   1.33    t/1.5   =   ln1.33   =   0.2877    time   t   =   1.5* 0.2877   =   0.431   s    b.   CR   =   1.5   s          C   =   1.5/ R   =   1.5 / 250 *103      =   6.0*10-6   F   =   6.0   F

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