Question

21. [3pt) An open switch, a 6,12 kohm resistor and a 3.87 microfarad capacitor are connected in series across a 22.5 V battery. The capacitor starts with no stored char Find the time constant. Answer: Last Answer: 0.002368 Not yet correct, tries 1/10 Submit All Answers 22. [3pt) Once the switch is closed, how long will it take to fully charge the capacitor? Answer: 23. [3pt) The capacitor has no charge. The switch is closed. How long will it take for the capacitor to charge up to 70 percent of full charpe Answer: Submit All Answer

Answer 1

1) We know that the time constant

T= RC

here R=6.12*10³ ohms , C=3.87*10^-6 F

T = 6.12 * 10% * 3.97 * 10-6

T= 23.6844 * 10-3

T=0.02368445

2) time taken by the capacitor to full charge

t = 5т

t = 5*0.0236844 = 0.13422

t = 0.13422s

3) We know that for charging capacitor

Q=Q.(1-e-t/RC)

Q=70Q_o/100 =0.70Q_o

put that  value in equation 1

0.70Q_o =Q_o(1-e^-t/RC)

0.70=1-e^-t/RC

e^-t/RC =0.3

take ln both side

t=-RC ln(0.3)

t=-0.0236844 ln(0.3)

t=0.02852 s