Question

Remaining Time: 2 hours, 47 minutes, 15 seconds. Question Completion Status: Path:p QUESTION 25 Consider the circuit below and answer the following questions. In this sketch, V=6 V, R=3000, and C=10 micro-F. C a) What is the maximum charge the capacitor can store in this circuit? b) How much energy will the capacitor store when it holds the maximum charge? c) How long will it take to charge the capacitor to half its maximum charge? Assume it starts with no charge stored. Please write your answers in the space below and email your work. Τ Τ Τ Arial + 3 (12pt) T E- i's Path: P QUESTION 26 Click Save and Submit to save and submit. Click Save All Answers to save all answers.

Answer 1

a) Total charge stored in the capacitor is given by

$Q=Capacitance\times Voltage=10\times6\ \mu C=60\ \mu C$

b) Energy stored is given by

4 E J. (60 x 10-6) 2 × 10 × 10-6 J = 1.8 x 10-4 J 20

c) For an RC circuit, charging is given by

$Q=Q_0\left ( 1-e^{-\frac{t}{RC}} \right )$

Q0 is the maximum charge and t is the time at which charge is zero

We need to for which Q=Q0/2 i.e.,

$\frac{Q_0}{2}=Q_0\left ( 1-e^{-\frac{t}{RC}} \right )$

$or,\ e^{-\frac{t}{RC}}=\frac{1}{2}$

$or,\ \frac{t}{RC}=\ln 2$

$or,\ t=RC\ln 2=300\times10\times10^{-6}\times \ln 2\ s=2.08\times10^{-3}\ s=2.08\ ms$